Lightly spoon masa harina and flour into dry measuring cups; level with a knife. Combine masa harina, flour, baking powder, and salt in a medium bowl; cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add broth; stir just until moist. Turn dough out onto a lightly floured surface; knead lightly 5 or 6 times.
Divide dough into 6 equal portions. Shape each portion into a ball. Press each ball into a 6-inch circle on a lightly floured surface (cover remaining balls to prevent drying). Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Place 1 gordita in pan; cook 2 minutes on each side or until lightly browned. Remove gordita from pan; cover and keep warm. Repeat the procedure with cooking spray and remaining gorditas.
Place beans in a bowl; mash with a fork to desired consistency. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add beans; cook 2 minutes, stirring frequently. Stir in salsa verde; cook 2 minutes or until liquid almost evaporates, stirring frequently.
Combine avocado and lime juice; toss gently to coat. Spread about 1/4 cup bean mixture on each gordita; top with about 2 1/2 tablespoons Pork Carnitas and 2 teaspoons avocado mixture. Sprinkle 1 teaspoon onion and 1 teaspoon chopped cilantro over each serving. Garnish with cilantro sprigs, if desired.