Place the diced sweet potatoes in a microwave-safe bowl with 1 tablespoon of olive oil, cumin, chili powder, salt, and pepper. Microwave on high for 6 to 8 minutes, stirring once, until the pieces are tender.
Mash the sweet potatoes lightly in the bowl, then stir in the black beans until evenly combined.
Heat a large skillet over medium heat and add ½ tablespoon of olive oil. Place one tortilla in the skillet and sprinkle ¼ cup of cheese over half of it.
Spread about ½ cup of the sweet potato and black bean mixture over the cheese, then add another ¼ cup of cheese on top. Fold the tortilla in half and cook for 2 to 3 minutes per side until golden and the cheese melts. Repeat with the remaining tortillas and filling, adding more oil as needed.
Cut each quesadilla into wedges and top with sliced avocado before serving.