1. Sauté onion in 1 Tbsp. hot oil in a small skillet over medium-high heat 4 minutes or until tender. Stir in garlic. Remove from heat.
2. Prepare Avocado-Corn Salsa; chill until ready to serve.
3. Mash together taco seasoning and 2 cups black beans in a large bowl with a fork. Stir in panko, next 2 ingredients, onion mixture, 1 cup pepper Jack cheese, and remaining black beans until well blended. Shape mixture into 6 (1/2-inch-thick) patties.
4. Cook patties in remaining 3 Tbsp. hot oil in a large nonstick skillet over medium heat 4 to 5 minutes on each side or until golden brown.
5. Preheat oven to 400°. Place tostadas on a 15- x 10-inch jelly-roll pan; top with Cheddar and remaining pepper Jack cheese. Bake until cheese melts. Top with black bean cakes and salsa.