In a large pot, heat some oil over medium heat and add the diced onion and bell pepper. Cook until softened, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the ground venison and cook until browned, about 8-10 minutes, breaking it apart with a spoon.
Sprinkle the chili powder, cumin, smoked paprika, salt, and pepper over the browned meat and stir well to combine.
Pour in the crushed tomatoes and beef broth, stirring to combine all the ingredients.
Bring the mixture to a simmer, then reduce the heat to low and cover the pot. Let it cook for 1-1.5 hours, stirring occasionally.
Add the drained kidney beans to the pot during the last 15 minutes of cooking and stir gently.
Taste and adjust seasoning as needed before serving hot with desired toppings.