Preheat and Prep: Heat the oven to 400°F. Line a baking sheet with foil. Dice the mango, then pit and chop the cherries.
Mix the Salmon Crust: In a bowl, stir together the flour, brown sugar, orange zest, salt, pepper, and sesame oil until it looks like damp sand.
Coat the Salmon: Place the salmon fillets on the prepared baking sheet. Press the brown sugar mixture evenly onto the top of each fillet.
Bake the Salmon: Bake until the salmon flakes easily and the topping looks set, about 10 to 12 minutes. Let the salmon rest for 2 minutes before serving.
Assemble the Quesadillas: Set aside about ½ cup of the chopped cherries for the quesadillas. Sprinkle cheese over half of each tortilla, add a spoonful of cherries, then add a small handful of arugula. Fold tortillas in half.
Cook the Quesadillas: Melt butter in a skillet over medium heat. Cook quesadillas until golden and the cheese is melted, about 2 to 3 minutes per side, adding more butter as needed.
Toss the Fruit Topping: In a bowl, combine the mango, the remaining cherries (about 1½ cups), basil, mint, and apple cider vinegar. Toss until evenly mixed.
Serve: Spoon the cherry-mango topping over the salmon and serve immediately with the warm savory cherry quesadillas.