Prick the sweet potato all over with a fork. Microwave for 5 minutes. Then flip and microwave for another 4 minutes. The potato is done when a fork slides into the side easily. Let cool for 5 minutes.
Remove the peel from the potato, and place the potato in a medium bowl. Mash lightly, and stir in the cumin, chili powder, and salt.
In another bowl, stir together black beans, chicken, and cilantro.
Heat a skillet or griddle over medium heat.
Lay all 12 tortillas on a work surface. Spread one side of each tortilla lightly with mayonnaise.
Place 6 tortillas, mayo-side down, in the skillet or on the griddle (you may need to do this in batches).
Spread 2 tablespoons of mashed sweet potato on each tortilla, and top with 3 tablespoons of the black bean and chicken mixture. Then, top with 3 tablespoons of cheese.
Cook for about 3 minutes, and once the bottom of each tortilla is golden brown, remove the tortillas from the skillet. Place the remaining tortillas on top of the cheese, mayo-side up. Carefully flip the quesadillas over and place them back in the skillet, mayo-side down. Cook for 2 minutes longer, or until golden brown on the bottom and the cheese has melted.
Serve the quesadillas with pico de Gallo or as desired.