Preheat oven to 450 degrees F (230 degrees C). Cut several slashes into each sweet potato.
Bake the potatoes in the preheated oven until tender, about 45 minutes. Mash the hot sweet potatoes in a bowl. Reduce oven heat to 200 degrees F (95 degrees C).
Heat a skillet over medium heat, and warm a tortilla in the skillet until pliable, about 2 minutes. Flip the tortilla over, and sprinkle the tortilla to about 1/2-inch of the edge with 1/3 cup of shredded Cheddar cheese. Allow the cheese to melt, and spread about 1/3 cup of mashed sweet potato over the melted cheese. Spread 2 or 3 tablespoons of black beans over the sweet potatoes. Fold the tortilla in half, enclosing the filling. Repeat with the rest of the tortillas; keep filled quesadillas warm in the oven.
