Preheat a large skillet over medium heat.
In a large bowl, combine the barbecue sauce, molasses, beet juice, chili powder cumin, and black pepper. Stir in the beans and cooked brown rice until fully combined. Add more egg white if needed to bind them together.
Shape the mixture into four patties and brush each side with olive oil.
Place the burgers in the skillet and cook for about 5 minutes on each side, or until the outside is golden brown and crispy.
Add a slice of cheese to the top of each burger during the last minute of cooking, allowing it to melt.
Serve with your favorite toppings, like lettuce, tomato, and onion slices.