In a large bowl, add about half of the rinsed black beans.
Using a potato masher or fork, mash them into a coarse paste. This will act as the binder for your patties.
Add the remaining whole black beans, drained corn, crushed corn chips, cooked rice, red onion, 1/2 cup (480 ml) salsa, chipotle peppers, cumin, and minced garlic to the bowl.
Stir everything together until just combined—be careful not to overmix!
Divide the mixture into 8 equal portions and shape them into patties about 3/4-inch thick.
Brush both sides of each patty with olive oil.
Place the patties on a tray, cover, and chill in the refrigerator for at least 1 hour to help them firm up.
Preheat your grill to medium heat.
Place the patties on a grill pan set directly on the grill rack. For a charcoal grill, cook over medium coals for 8-10 minutes. For a gas grill, cover and cook for 8-10 minutes.
Flip the patties once, halfway through, until they are heated through and nicely browned.
While the burgers are grilling, warm the tostada shells according to the package directions.
To serve, place a grilled patty on each warm tostada shell. Pile high with shredded cabbage, extra salsa, radishes, cilantro, and any other desired toppings like queso fresco or avocado.
Serve immediately with lime wedges on the side.