Quarter mushrooms. Core Roma tomato and cut into ¼" dice. Halve and peel onion. Slice half into thin strips (julienne) and cut remaining half into ¼" dice. Zest and halve lime. Quarter one half and juice remaining half. Drain and rinse beans in wire-mesh strainer.
Make the Beans
Place a medium pot over medium heat. Add 1 tsp. olive oil and diced onion to hot pot and cook 1 minute, or until aromatic. Add beans and ¾ cup water to pot and cook 6-10 minutes, or until warmed through and tender. Coarsely mash beans with potato masher or fork until thickened, but still spreadable. About half the beans should remain whole. Taste, and season with a pinch of salt and pepper, if desired.
Cook the Mushrooms
While beans are cooking, place a medium non-stick pan over medium-high heat. Add 2 tsp. olive oil, mushrooms, half the sliced onions, and smoked paprika to hot pan and cook, stirring occasionally 7-11 minutes, or until well-browned. Remove from burner.
Bake the Tortillas
Spray both sides of four tortillas with cooking spray and place on baking sheet. Bake 6-8 minutes, or until crisp and toasted. Set aside.
Make the Cabbage
Combine red cabbage, remaining sliced onions, 2 tsp. lime juice, ½ tsp. lime zest, and 1 tsp. olive oil in a mixing bowl. Halve avocado and remove pit by carefully tapping pit with the blade of your knife so it sticks. Gently twist knife to release pit. Scoop out the flesh with a spoon. Cut into ¼" slices. Preparing avocado later in the recipe helps prevent it from oxidizing.
Plate the Dish
Assemble tostadas in this order: tortilla, black beans (you may not use all the black beans), red cabbage slaw, sliced avocado, sour cream, and diced tomato. Garnish with any remaining lime zest and lime quarters.