Heat a large (at least 5.5-quart) Dutch oven or heavy bottomed pot over medium-high heat with 1 Tbsp olive oil. Once hot, add the bison and cook for 4-5 minutes to brown one side before breaking apart and fully cooking. Use a slotted spoon or spatula to transfer the cooked bison to a bowl and set aside.
Add the remaining olive oil to the pot, followed by the onion, peppers, carrots, and 2 tsp salt. Cook until the veggies begin to soften, about 8-10 minutes. Stir in the garlic and tomato paste. Cook for 1-2 minutes until fragrant.
Add the cooked bison to the pot along with the beer. Deglaze and cook until very little liquid remains, about 4-5 minutes.
Stir in the chili seasoning, followed by the crushed tomatoes, broth, and bay leaves. Bring to a boil before reducing the heat to low, covering, and simmering for 2-3 hours (the longer, the better). Stir the chili every 30-45 minutes.
Before serving, stir in some chopped herbs like chives, parsley, oregano, or dill and a splash of vinegar. Salt and pepper to taste.