Step 1: In a large Dutch oven or heavy-bottomed pot, heat the olive oil (or rendered brisket fat) over medium heat. Add the diced onion and cook until softened and translucent, about 5-7 minutes.
Step 2: Add the minced garlic to the pot and cook for another minute until fragrant, being careful not to burn it.
Step 3: Stir in the chili powder, ground cumin, smoked paprika (if using), and cayenne pepper. Toast the spices for about 30 seconds, stirring constantly, until fragrant.
Step 4: Pour in the beef broth (or beer) and scrape the bottom of the pot with a wooden spoon to loosen any browned bits. Allow the liquid to come to a simmer for 2-3 minutes.
Step 5: Stir in the fire-roasted diced tomatoes, regular diced tomatoes, tomato paste, and Worcestershire sauce. Add the rinsed and drained kidney and pinto beans (if using). Bring the mixture back to a gentle simmer.
Step 6: Add the shredded or diced leftover brisket to the pot. Stir well to combine, ensuring all the brisket is submerged in the chili base.
Step 7: Reduce the heat to low, cover the pot, and let the chili simmer for at least 45 minutes to 1 hour, or even longer for deeper flavor. Stir occasionally to prevent sticking.
Step 8: Taste the chili and adjust seasonings as needed with salt, pepper, or additional spices. If the chili is too thick, add a little more beef broth; if too thin, simmer uncovered for a bit longer. Serve hot with your favorite toppings.