Heat oil in a large skillet over medium-high heat. Season shrimp with salt and pepper. Add shrimp to hot skillet and cook for 2 to 3 minutes per side, until no longer pink. Remove shrimp from pan and set aside on a cutting board to cool.
In a medium bowl, mix together the cream cheese, cheddar cheese, and cilantro with a spoon until evenly combined. If you don't like cilantro, substitute chopped green onion instead.
Chop cooled shrimp into small pieces.
Heat a large skillet over medium heat. (I use the same on the shrimp was cooked in and wipe it out before reusing.) Spread 1 tablespoon of butter on one side of a tortilla. Place the tortilla in the skillet buttered side down.
Carefully spread 1/4 of the cream cheese mixture over half of the tortilla. Top the cheese mixture with 1/4 cup of shrimp and 1/4 cup of mango. Using a spatula, fold the tortilla in half, over the filing. Cook for 2 to 3 minutes per side until tortilla is golden brown and the filling is gooey.
Remove your quesadilla from the skillet, and cut it into 4 or 8 wedges. Repeat with the remaining ingredients. Serve immediately.
I've also made this recipe using 8-inch tortillas and it made a total of 5 quesadillas. Yield will vary based on the size of your tortillas.