Epic! and a little game theory, too.
A few apple and orange comparisons are at work here. First, there's the physical camp that seems to imply that having a lot of components, chromy things, and large ruleset define an epic game. There's another line of thought that plays out on more of an emotional level, along the lines of "starting small but finishing huge." Finally, there's the third line of thought that is sort of "well, I've played games of chess that I'd consider Epic."
First of all, I think we can dispose of dealing with the third case. This is merely dealing with the concept of EPIC TALES THAT WILL BE TOLD FOR YEARS, and interesting stories about an event. Indeed, I suppose you could have an epic battle of between people playing tic-tac-toe, constantly playing to draws for hours on end, until sleep depravity (or the need to go to the bathroom) drove one player make a bad play. For the most part, these are merely legendary stories; and I don't think anyone can freely call the design of tic-tac-toe epic in any sense, even though one could, I suppose, have an epic game of it.
Which I guess leaves us at with the first two lines of thought.
In my mind, if the real goal was to answer the question of "How do I go about designing an Epic game," my answer would fall along the second line. I think that you have to start out with the notion that you are going to try to make a game, thematically, where the player has lofty, thematic goals, but they start out as a lowly peasant (or a thematic equivalent). This is the traditional epic quest, the heroes quest, if you will.
While I suppose one could study Joseph Campbell's seminal work on this subject, The Hero of a Thousand Faces, it's probably overkill for game purposes. There's a lot of stages the hero goes through, and it's pretty far beyond the scope of a typical boardgame.
However, if one COULD create a game that follows the Campbell roadmap to the letter, it would be truly EPIC!!!!! indeed.
Anyway, thematically "starting small with large goals" leads pretty much to the first line of thought anyway as a consequence. You'll be needing all those shiny, plasticy pieces to keep track of your ever-growing armies; or those well-illustrated cards indicating your new actions you've acquired or learned and can apply. Simply put, I don't think you can have huge goals while starting small WITHOUT a lot of components for keeping track of how large you've gotten, or how close to the lofty goal you've become.
The next thing to question would be, "can the theme itself somehow keep a game from being epic?" I suppose it could...but I think a sense of something being epic leads a person to looking back at the end of the game and seeing what they have accomplished. And for any game to have an epic feel, the accomplishment of starting gamewise from a lonely peasant boy to becoming the CEO of a cotton ball factory (assuming cotton ball manufacturing is, indeed, your theme), still allows you to look back and see all the little accomplishments along each step of the way.
Additionally, the amount of time spent should matter. There is very little epic-ness in completing a game in 15 minutes to start all over again. Going on an epic quest means having to spend something dearly to achieve the goal. Beyond the purchase price of a game, there is very little spent on the game aside from time.
Time seems to be a fairly good constant with regards to this. The struggles between a baseball better who constantly is fouling balls off a pitcher with two strikes against him seems to always be raising the ante; who will give in first? The above mentioned game of the theoretical tic-tac-toe game that goes on for days will have an epic quality to it; they've both spent so much in terms of time, who will win the battle after spending all that time and energy?
There's actually a good "game theory" theory about this. Sure, everyone has heard of "The Prisoner's Dilemma." But in real life, the Prisoner's Dilemma is hard to play out since the results are way too dramatic. There are very few real life examples that play out nicely in PD (well, unless you go on crime sprees, and your ONLY concern is the amount of time you do in prison).
The game theory that I suggest that is worth looking at is called "The Dollar Auction." There is a large element of epic in here, in that it deal specifically with a person's amount of willingness to press something being spent, with the possibility of getting nothing in return.
And, you can actually play it at home with a reasonable outcome, which is something PD won't let you do.
Basically, a person puts a dollar up for auction. Players can bid on it, starting at a penny. The trick is that once all players have quit, and one person has made the top bid, both the top bid AND second highest bidder pay their bids. What usually happens is this: both players wind up paying more than a dollar for the dollar. It becomes more about the money spent while gaining nothing in return than trying to make a profit.
This plays out in life all the time; how much of something are you will to pay in the hopes that you won't get nothing at all. Do you wait in a really long line for tickets that might be sold out by the time you get there? You want a Wii, but you can only go to either Best Buy or Toys R Us, because odds are, if you go to one store, the other one will be sold out. Do you spend the night waiting in line in the hopes that there will be one available? People waiting in lines for days when the iPhone came out are really pretty stupid, but epic in some sense, I suppose, in that their story became a legend of some sorts. Even though I would like to think that all that time spent on a piece of tech could've been spent better elsewhere.
Of course, you could not play at all, but that's not very epic. But spending a LOT of something for an accomplishment, however small, is pretty epic. And the something should be a tangible personal investment. Little pieces of cardboard that have no value in real life isn't much of an investment; the only thing a person playing a game can tangibly invest is time.
So, there you go! "Start small, big goals, and a fairly large chuck of time."