Heat oil in a large stock pot or Dutch oven over medium-high heat until shimmering. Add onions, bell pepper, chili powder, cumin, coriander, oregano, thyme, cayenne pepper, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cook until vegetables have softened, 7 to 10 minutes.
Stir in garlic until fragrant, about 30 seconds. Add venison and cook, breaking up the clumps with a spoon, until the venison is no longer pink, about 5 minutes.
Stir in kidney beans, tomatoes, and tomato puree. Bring to a simmer, cover, and cook for 30 minutes.
Remove lid and continue to simmer for 30 minutes longer. Season to taste with salt and pepper.
Serve with preferred toppings including cheese, sour cream, and scallions.