Preheat the broiler. Rinse and drain the beans. Puree the black beans, chili powder, cumin, and cayenne in a blender or food processor, adding a tablespoon of water at a time to help the mixture move, if necessary. I ended up using about 2 tablespoons water and pureed for a minute or two but still left some texture.

In a food processor or blender, puree the cilantro, yogurt, garlic, and salt, adjusting the seasoning with more cilantro/salt/yogurt to your taste.

Place tortillas in the oven directly on the rack, taking care that the edges are all supported by the rack (otherwise they will bend through the cracks and it will be bent in a funny shape). Let the tortillas bake for 3-5 minutes on both sides until they are browned and crispy.

Top the crispy tortillas with black beans, tomatoes, avocados, and lettuce. Drizzle with cilantro sauce.

Notes:
Holding the tostadas while you spread the bean mixture helps them not to break apart.
Other topping ideas include cotija cheese, lime wedges, salsa, ranch dressing, or roasted corn or peppers.