Spread goat cheese on tortillas. Divide mango, onion, and cilantro on one half of each tortilla. Fold tortilla over filling. {alternatively, if you're really hungry, you can use 2 whole tortillas and just put one on top of the other.}

Heat a large heavy skillet over medium-high. Working in batches, cook quesadillas until cheese softens and tortillas are crisp and browned in spots, 1 to 2 minutes per side (if skillet begins to scorch, reduce heat to medium). Transfer quesadillas to a cutting board and cut each into 4 wedges. Serve immediately.