Pan-fry the onions and peppers. Preheat your stove to medium heat with a large dutch oven or cast iron pot.
In a large skillet, drizzle the olive oil and mix in the diced peppers and onions. Cook for 5-6 minutes, or until the peppers are tender and the onions are transparent. Cook for another couple of minutes after adding the garlic.
Add the other ingredients to the brisket chili. Toss in the chopped brisket and toss gently in a stockpot until everything is well mixed.
Combine the beans, tomatoes, green pepper, and seasonings in a large mixing bowl. Taste and season with additional salt, pepper, chili powder, or other seasonings if necessary. Stir until everything is thoroughly blended.
Cook the chili. Reduce to a low heat setting and cover. Allow for at least 30 minutes, or up to 2 hours, of cooking time, stirring occasionally.
Serve right away. Garnish the cooked brisket chili with grated cheese, diced onions, sour cream, or your favorite toppings!