Add the carrots, onion, and garlic to a food processor. Pulse until everything is finely chopped.
Add the ground beef and breakfast sausage to a large mixing bowl. Add the carrot mixture to the beef along with the bbq sauce, shredded cheese, salt, pepper, onion powder, and garlic powder.
Mix until evenly combined. Then divide the beef mixture into 12 equal portions. (You can eyeball it. They should be around 1/3 pound each.) Then use your hands to form hamburger patties. With your knuckle, indent the center of the patties (this helps to keep them flat when cooking).
Preheat your grill (or grill pan on the stove) to medium-high heat. You can also use a cast iron skillet over a campfire. Once hot, cook the burgers for 4-6 minutes per side for medium doneness.
To assemble: Place one or two burger patties on the bottom bun. Top with lettuce, tomato, and/or pickles. Spread some ketchup and mayo on the cut side of the top bun before placing it on the burger. Serve warm.
Notes
Nutritional information is for 1 patty on a bun with 1 lettuce leaf, 2 tomato slices, 4 pickles, and 1 tbsp each ketchup and mayo.
You can lean into the BBQ flavors of the patties and top your burger with cooked bacon slices, onion rings, and a little extra bbq sauce on the bun too.