I have a bunch of chili recipes, because every time I make chili, I do something different.
With leftover meat, it's all about the soup/sauce. The cooked meat doesn't require browning, but I do sauté the onions. I add chopped garlic about a minute before the onions are done. Cube the meat, then depending how much meat I use, I add canned crushed or diced tomatoes, preferring diced. Then in goes salt, black pepper, cumin, chili powder, paprika, and cayenne pepper. I just use the palm of my hand to measure. The ratios are 1-1-2-2-1-1/4. Add some beef stock if it is too thick. Simmer covered with the lid cracked open a tad for an hour. Check that the meat falls apart, and serve.
A couple things I do to mess with my chili loving friends is add some browned breakfast sausage filling and a teaspoon of sugar.
If you have dried chilies in your area, skip the chili powder and reconstitute about 6 Anaheim or Pasilla or New Mexico chilies. Drain, blend, and add to the soup/sauce.
Beans are totally optional. My wife likes beans in her chili. I'll use a can or two of black beans (less gas).