Place black beans in a medium bowl; mash with a fork. Stir in 1/2 cup finely chopped cilantro and the next 7 ingredients (through egg whites). Shape bean mixture into 6 (1/2-inch-thick) patties. Arrange patties on a baking sheet coated with cooking spray. Bake at 350° for 20 minutes, carefully turning once.
Combine remaining 1/4 cup cilantro, mango, and the next 4 ingredients (through minced garlic) in a medium bowl. Place a patty on bottom half of each hamburger bun; top each with 1 lettuce leaf, 1/3 cup salsa, and top half of bun.