Heat the oven to 425°F and line a large rimmed baking sheet with parchment paper.
Cut the sweet potatoes into 1/2-inch rounds, leaving the skins on. In a large bowl, toss them with the olive oil, smoked paprika, cumin and 1/2 teaspoon salt until evenly coated.
Arrange the rounds in a single layer on the baking sheet. Roast for 20 minutes, flip each round, and roast 8 to 10 minutes more, until tender and browned at the edges.
While they roast, stir the Greek yogurt with 1 tablespoon of the lime juice and a pinch of salt. Add a teaspoon of water if needed so it drizzles.
Warm the black beans and corn in a small skillet over medium heat for 3 to 4 minutes, then stir in the remaining lime juice and a pinch of salt.
Spoon the bean mixture onto the warm sweet potato rounds and top with the feta.
Drizzle with the lime crema, scatter the cilantro over the top, and serve warm.