Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season the chuck roast pieces with salt and pepper. Sear the beef in batches until browned on all sides. Remove and set aside.
Add the onion and bell peppers to the same pot and cook for 5 minutes until softened. Add the garlic and cook for 30 seconds until fragrant.
Stir in the tomato paste, chili powder, smoked paprika, cumin, oregano, salt, black pepper, and cayenne pepper. Cook for 1 minute to toast the spices.
Return the chuck roast to the pot. Add the crushed tomatoes, beef broth, Worcestershire sauce, and brown sugar if using. Stir well to combine.
Bring to a simmer, then reduce heat to low. Cover and cook for 2 ½ to 3 hours, stirring occasionally, until the chuck roast is tender and pulls apart easily.
Remove the lid during the last 30 minutes to let the chili thicken. Stir in the kidney beans and pinto beans during the last 20 minutes.
Taste and adjust seasoning as needed. Serve warm with your favorite toppings.