Heat the bacon grease or other oil in a large Dutch oven over medium heat. Add the beef and cook until mostly cooked through with a little pink remaining, breaking up any clumps with a wooden spoon.
Add the onions, garlic, chili powder, cumin, salt, pepper, and cayenne, and cook until fragrant, one more minute. Stir in the tomatoes.
Reduce the heat to low and simmer for 30 minutes. Add the cauliflower and continue to cook until tender, another 15 minutes or so.
Add the cheese and stir in until melted. Serve with your favorite chili toppings such as sour cream and avocado.