Start by cooking the turkey or bison in a 4 quart dutch oven or similar sized deep skillet or saucepan, something that will eventually hold your pot of chili. (Heat pan, drizzle in half of the oil and add the meat. Chop up into lumps and let cook until browned before turning and cooking the other surfaces. When completely browned, remove from pan onto a plate.)
Add remaining oil to pan and let it heat. Add chopped onion and green pepper and cook until softened, about 5 minutes.
Add tomato paste and stir with a wooden spoon or spatula to cook it a minute. Add garlic, green chiles, water, pinto beans, tomatoes and seasonings. Add the meat you browned in step 1. Simmer gently for “awhile”...15 minutes or so if you’re trying to get the crowd fed, or longer (like 30 - 45 minutes) if you have some time on your hands. (While simmering you can cut at the tomatoes with kitchen shears to get them into smaller pieces.) Serve with grated cheddar cheese, sour cream and some cornbread or tortillas.