Heat 2 tablespoons olive oil in a large pot over medium heat until shimmering.
Add 1 large yellow onion (diced), 2 cloves garlic (minced), 1 red bell pepper (diced), and 1 green bell pepper (diced). Sauté, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add 2 pounds cooked brisket (trimmed and cut into 1/2-inch cubes) to the pot. Sprinkle in 2 tablespoons chili powder, 1 teaspoon ground cumin, 1/2 teaspoon smoked paprika, 1/4 teaspoon cayenne pepper, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper. Cook, stirring, for 2 minutes to coat the meat with the spices.
Stir in the drained, rinsed 115-ounce can kidney beans and the drained, rinsed 115-ounce can black beans, the 128-ounce can crushed tomatoes, and 2 cups beef broth. Stir until combined and bring the mixture to a gentle simmer.
Reduce the heat to low, cover the pot, and let the chili simmer gently for 2 1/2 to 3 hours, stirring every 20–30 minutes to prevent sticking and to help flavors meld.
Remove from heat and ladle the chili into bowls. Serve hot topped with shredded cheddar cheese, chopped green onions, and sour cream, if desired.