Preheat the oven to 425°F (220°C).
Peel and dice the sweet potatoes into 1-inch cubes. Toss them with olive oil, cumin, paprika, salt, and pepper in a medium mixing bowl until evenly coated.
Spread the sweet potatoes on a baking sheet in a single layer. Roast in the oven for about 20-25 minutes, or until they are tender and slightly caramelized, stirring halfway through.
While the sweet potatoes are roasting, heat a large skillet over medium heat. Add the black beans, chili powder, and a pinch of salt. Cook for about 5 minutes, stirring occasionally until heated through.
Once the sweet potatoes are done roasting, remove them from the oven and set aside.
To assemble the tostadas, layer each tostada shell with a generous spoonful of black beans, followed by the roasted sweet potatoes.
If desired, sprinkle with crumbled feta cheese and garnish with fresh cilantro.
Serve with lime wedges on the side for squeezing over the tostadas.