If you cook a roast or steak just for this purpose, a crock pot is the best way to go. I will put one or two roasts (or steaks depending on what's on sale) in mine, fill it with water covering the roast, add cumin, garlic and onion, and put on low heat and cook over night.
This will also give you a large amount of beef stock-a two for one! If you do cook it over night, you may need to re-season before serving.
Place shredded beef and chili in skillet or pot. You only want enough chili to "coat" the beef, and drain off any excess liquid before combining the two.
Mix together well and heat for about 20 minutes to distribute the flavor of the chili to the beef.
Heat the tortillas in the micro for about 1-2 minutes, depending on how many you are using. You want them to be pliable so when you roll them they do not crack or break.
Place cheese in center of tortilla. You can use as much or little as desired.
Place about 3 tbs. of chili beef in center. You could always add chopped onions, tomatoes and/or jalapenos at this point. Be sure to leave about 2" on each side of the tortilla so you can fold in the sides.
Fold over both sides and roll the tortilla up. Place seam side down on a tray.
Heat about 2" of oil in cast iron or heavy skillet, heat to med. high, or frying temp.
Place chimi seam side down in oil and fry for about 1-2 minutes. With tongs, turn over and fry other side. If you don't have enough oil to halfway submerge your chimi, lay on each side to fry.
Serve with red or green salsa, sour cream or additional cheese.
These wrap great in foil and are easy to take on the road