Place the cubed sweet potatoes in a microwave-safe bowl with a splash of water. Cover and cook for 6 to 8 minutes until soft, then mash lightly with a fork.
Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and cook for 3 minutes until softened.
Stir in the black beans, cumin, chili powder, and salt. Add the mashed sweet potatoes and mix until the filling is well combined and warmed through, about 2 minutes. Remove from heat.
Lay out four tortillas and sprinkle half the cheese over them. Divide the filling evenly on top, then add the remaining cheese and cover with the other four tortillas.
Wipe the skillet clean if needed and melt half the butter over medium heat. Cook each quesadilla for 2 to 3 minutes per side until golden and the cheese melts. Repeat with the remaining butter and quesadillas.
Cut into wedges and serve right away.