In a medium bowl, combine the mashed sweet potato, shredded Monterey Jack cheese, black beans, red onion, ground cumin, chili powder, and kosher salt until evenly mixed.
Lay one tortilla flat on a clean work surface and spread half of the sweet potato mixture evenly over one half of the tortilla, leaving a 1/2-inch border around the edge.
Fold the empty half of the tortilla over the filling to create a half-moon shape, pressing gently to seal the edges.
Heat a large non-stick skillet or griddle over medium heat and add 1 tablespoon of butter, swirling to coat the surface.
Place one filled quesadilla in the skillet and cook for 3-4 minutes until the bottom is golden brown and crisp, then carefully flip using a spatula.
Cook for another 3-4 minutes on the second side until golden brown and the cheese inside is fully melted.
Transfer the cooked quesadilla to a cutting board and repeat the cooking process with the remaining butter and second quesadilla.
Let the quesadillas rest for 2 minutes before slicing each into 3 wedges for serving.