Combine cubed buns, beans, and tomato paste in a large bowl; using a potato masher, mash to slightly chunky consistency.
Add ground beef, onion, cilantro, jalapeño pepper, cumin, salt, and pepper, mixing lightly but thoroughly.
Lightly shape into eight 3/4-inch thick patties.
Place patties on rack of broiler pan so surface of beef is 3–4 inches from heat.
Broil 12–14 minutes until instant-read thermometer inserted horizontally into center registers 160 degrees, turning once.
Place burgers on bottoms of buns.
Top burgers evenly with avocado slices.
Top with dressing, sour cream, yogurt, or salsa, if desired.
Cook’s Tip: This burger may be served on a bed of mixed greens topped with your favorite salsa. Cooking times are for fresh or thoroughly thawed ground beef. Ground beef should be cooked to an internal temperature of 160 degrees. Color is not a reliable indicator of ground beef doneness.