Preheat your oven to 425°F (220°C) and arrange racks in the upper and lower thirds of the oven.
Prepare the butternut squash by tossing the cubes with 1-2 tablespoons olive oil, chipotle powder, salt, and pepper on a baking sheet. Spread in a single layer and roast for 20-25 minutes, stirring halfway through, until tender and caramelized at the edges.
While the squash roasts, prepare the beans. Heat 1 tablespoon olive oil in a skillet over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic to the skillet and cook for 30 seconds until fragrant, being careful not to burn it.
Stir in black beans, cumin, oregano, and smoked paprika with a splash of water (about ¼ cup). Simmer for 5-7 minutes, mashing some beans slightly with a wooden spoon to create a partially creamy texture. Season with salt, pepper, and lime juice.
While the beans simmer, prepare the tostada shells. Lightly brush both sides of corn tortillas with olive oil and place them directly on the oven rack or on a baking sheet. Bake for 4-6 minutes until crisp and lightly golden, watching carefully to prevent burning.
Assemble your tostadas by spreading a layer of black bean mixture on each crispy tortilla, followed by the chipotle butternut squash, avocado slices, crumbled cheese, red onion, and fresh cilantro.
Serve immediately with hot sauce or Mexican crema if desired, and extra lime wedges on the side.