Peel and cut the sweet potatoes into 1" dice. Use a pot and a steamer basket to steam the sweet potato for 12-15 minutes, or until soft.
Transfer the sweet potatoes to a bowl. Mash them with a fork or a potato masher until smooth. Add the black beans and stir to combine.
Heat a large, slightly oiled skillet over medium heat. Fold a tortilla down the center to crease it and place it in the pan. Spread half with the sweet potato-black bean mixture. Topping with cheddar cheese. Fold over the other half of the tortilla. (Note: You can make the quesadilla with two tortillas, one on top of the other, but I find it much easier to flip them when folded.)
Cook the quesadilla for 3-5 minutes, or until browned and crispy. Flip and cook the other side until browned and crispy.
Fill and cook other tortillas as explained above. If desired, keep them warm in a 200 degree oven until ready to serve.