Place chiles on a foil-lined baking sheet; broil 3 inches from heat 8 minutes or until blackened and charred, turning after 6 minutes. Place in a heavy-duty plastic bag; seal. Let stand 15 minutes. Peel and discard skins. Cut each chile lengthwise into 4 strips; discard seeds.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add onion and garlic; sauté 5 minutes. Place onion mixture, salt, beans, and hominy in a food processor; pulse until coarsely ground. Combine bean mixture and 1/2 cup masa in a medium bowl. Divide bean mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty. Place remaining 1/4 cup masa in a shallow dish; dredge patties in masa.
Heat oil in skillet over medium heat. Add patties to pan; cook 4 minutes. Turn patties over. Top each patty with 3 tablespoons cheese; cook 4 minutes.
Combine sour cream and salsa in a small bowl. Spread 1 tablespoon sour cream mixture on top half of each bun. Place patties on bottom halves of buns; top each serving with 2 pepper strips. Cover with tops of buns.