To prepare sauce, combine the first 4 ingredients on a jelly-roll pan coated with cooking spray. Broil 12 minutes or until blackened, stirring once. Cool slightly. Place tomatillo mixture in a blender; add avocado, 1/4 cup cilantro, juice, and 1/2 teaspoon salt. Process until smooth. Cover and chill.
Preheat oven to 400°.
To prepare cakes, place bread in a food processor; pulse 10 times or until coarse crumbs measure 2 cups. Combine 1 cup breadcrumbs, 1/2 cup onion, and next 9 ingredients (through egg whites) in a large bowl; stir until well blended. Divide snapper mixture into 12 equal portions (about 1/4 cup each), shaping each into a 1/2-inch-thick patty. Dredge patties in remaining 1 cup breadcrumbs.
Melt butter in a large nonstick skillet coated with cooking spray over medium heat. Add cakes; cook 2 minutes on each side or until browned. Wrap handle of pan with foil; place in oven. Bake cakes at 400° for 8 minutes or until cooked through. Spoon about 2 1/2 tablespoons sauce on each of 6 plates; top sauce with 2 cakes.