Green chili LOVES pork (or for the health conscious, you could do chicken or turkey - just don't cook it as long!)
Buy a small to medium pork shoulder. Marinate it over night in tequila, lime, chopped garlic, cumin, salt and pepper. (you could cube it ahead of time if you want; if you want a little more flavor make sure there's a good amount of fat and you could throw in a few neck bones or rib scraps - i.e. 'riblets')
Get a half dozen to a dozen tomatillos (depending on size). If you can't find them, you can use green tomatoes, but you'll need to roast them first.
Buy a range of green chiles (season to taste: get more hot peppers [jalapenos, serranos, hueros, hatch/New Mexico, etc.) if you like the heat, more mild peppers [poblanos, Anaheim] if you don't). You will need poblanos no matter what - these are your base.
Cut open, remove seeds, stems and insides of all the peppers. Roast them up over an open fire. Make sure to blister all the skin. [you probably want to get yourself some good kitchen gloves to wear while cutting and roasting the peppers - especially the hot ones!]
Mix a pot of the leftover marinade, tomatillos (diced), and water and bring to a simmer. Throw in your roasted peppers and simmer them long enough that you can peel all the skins off.
Once you get the skins off the peppers (you can actually use a strainer or stirring spoon with holes to accomplish this over time), cube up your pork shoulder (or chicken/turkey) and throw it into the simmering pot (low heat). Throw in cumin, onion, garlic, oregano, epazote (go to the Mexican store or Mexican section of your grocery store - it'll likely be sold dehydrated), lime, and chopped cilantro to taste.
Stir often, don't cover the pot entirely for the first couple of hours. This will allow the stock to thicken a little bit. The more you stir, the more 'pulled' you pork will get and you can then fish out (or not) your neck bones, or other bones, etc. The chile is done once you're so hungry you can't wait anymore OR when the chiles have broken down enough that there are only slightly identifiable pieces swimming around in the pot.
Serve hot, with either tostada style corn tortillas w/sour cream and spicy green salsa OR with fresh warm corn tortillas. Also, some people like to eat bolillos (white bread rolls, also a slang word sometimes used for white folks - no offense) with this dish instead.
*Beans are nice to the side with some white rice or "sopita/Mexican" rice, but not in the chili.