Heat a large skillet over medium-high heat. Brown the ground beef and chuck roast in batches, transferring the browned meat to the slow cooker.
In the same skillet, sauté the onions and bell peppers until softened, about 5 minutes. Add the garlic and cook for another minute.
Transfer the vegetables to the slow cooker.
Add the diced tomatoes, tomato paste, beef broth, and beer (if using) to the slow cooker.
Stir in the chili powder, cumin, smoked paprika, oregano, salt, and pepper.
Cover and cook on low for 8-10 hours or on high for 4-6 hours.
About 30 minutes before serving, taste and adjust seasonings if needed.
Serve hot with your choice of toppings.