Brown the venison: In a large pot, heat some oil over medium-high heat. Add ground venison and cook until browned, breaking it up into small pieces. Drain any excess fat.
Add the vegetables: Add diced onion, garlic, and mixed vegetables (carrots, peas, and corn) into the pot. Cook until the vegetables soften and the onions become translucent, about 5-7 minutes.
Mix in the spices: Stir in chili powder, cumin, smoked paprika, salt, and black pepper. Stir well to coat the venison and vegetables evenly. Let the spices bloom for 2-3 minutes.
Simmer the chili: Add beef broth to the pot and stir to combine. Bring the mixture to a simmer, cover, and cook for 30-45 minutes, allowing the flavors to meld together.
Adjust seasoning and serve: Taste the chili and adjust the seasoning if needed. Serve hot with gluten-free cornbread or a side of your choice. Enjoy!