Heat 2 tablespoons of olive oil in your Dutch oven over medium heat. Add the diced yellow onion and cook until translucent and soft, about 5 minutes. Stir in the minced garlic, red bell pepper, and green bell pepper. Cook for an additional 3-4 minutes until the peppers soften slightly.
Add the cubed cooked brisket to the pot, mixing it well with the sautéed vegetables. Sprinkle in the chili powder, ground cumin, smoked paprika, cayenne pepper, kosher salt, and black pepper. Stir everything together to coat evenly. Let cook for 2-3 minutes to toast the spices and deepen flavor.
Pour in the drained kidney beans and black beans, followed by the crushed tomatoes and beef broth. Stir well to combine all ingredients. Bring the chili to a gentle simmer.
Reduce heat to low and let the chili simmer uncovered for 30-40 minutes. Stir occasionally, allowing flavors to meld and chili to thicken. This slow simmer will tenderize the brisket further and deepen the flavor.
Once the chili has thickened and flavors are well developed, taste and adjust seasoning if needed. Ladle chili into bowls and top with shredded cheddar cheese, chopped green onions, and a dollop of sour cream if desired. Serve hot with crusty bread or tortilla chips.