I get cynical responses when I tell people about this recipe, but once they taste the flavor combination, they're usually convinced. Make sure to slice the mango really thin, and if you're keen on substituting a different cheese in for this recipe know this: Muenster is king when it comes to quesadillas.
Season the skirt steak with salt and pepper, to taste, and rub with 2 tablespoons of the olive oil. Heat the last tablespoon in a small, nonstick sauté pan over high heat. Add the steak and brown on both sides until rare, about 2-3 minutes per side. Baste the steak while it is cooking by tipping the pan and spooning the juices from the oil back onto the steak. (If you want your steak more well-done, cook for 2 minutes longer on each side.)
Remove the pan from the heat and let the steak rest on a cutting board for at least 10 minutes. Lay 2 tortillas out on a flat surface and place 2 slices of Muenster cheese on both, so that the cheese slices look like a double diamond on the tortillas. Top each of the tortillas with about 5 slices of mango. Thinly slice the steak and add about 5 slices to each tortilla.
Pour out all but 1 tablespoon of the steak oil out of the pan and heat over medium-high heat. Add one of the assembled tortillas to the pan. Break up 1 slice of Muenster cheese and distribute evenly over the steak and the mango.
Then, add another 2 slices of Muenster cheese in the same double diamond formation as the bottom slices. Take another tortilla and lightly brush one side with olive oil, then top the layered tortilla in the pan with it, oiled side facing up.
Place a heavy bowl or pan over the quesadilla in the pan and cook for 1-2 minutes, until the bottom side of the tortilla is golden brown. Flip, top with the heavy bowl again, and cook for 2 more minutes.
Remove the quesadilla from the pan and let it rest on a cutting board while you repeat with the second layered tortilla. You may need to add more oil to the pan before starting the second quesadilla. Cut both tortillas into four equal slices and serve.