Preheat your oven to 400°F (200°C). Prick the sweet potatoes all over with a fork, place them on a baking sheet, and roast for 45-50 minutes until very tender when pierced with a knife. Let them cool until safe to handle, then scoop the flesh into a medium bowl and discard the skins.
Mash the roasted sweet potato flesh with a fork until smooth. Stir in the olive oil, cumin, chili powder, smoked paprika, salt, and black pepper until well combined.
To the sweet potato mixture, add the black beans, corn, red onion, and cilantro. Gently fold everything together until evenly distributed.
Lay the tortillas on a clean work surface. Divide the filling equally, spreading it over one half of each tortilla, leaving a 1/2-inch border. Sprinkle 1/3 cup of shredded cheese over the filling on each tortilla, then fold the other half over to create a half-moon shape.
Heat a large skillet or griddle over medium heat. Lightly brush the outside of one quesadilla with softened butter and place it in the hot skillet. Cook for 3-4 minutes per side, pressing down gently with a spatula, until the tortilla is golden brown and crispy and the cheese is fully melted. Repeat with the remaining quesadillas.
