Remove Brie from freezer to let warm up. Carefully remove skin from mango and cut away from seed as much of meat as possible (remember mangos have a flat seed, so you should be able to get 2 large meaty pieces) Carefully slice mango into thin strips. By this time the Brie has begun to thaw, and should slice easily into very thin strips. (Brie, being such a soft cheese, could never otherwise be sliced, unless frozen first.) Lay a tortilla on a work surface and place 2/3 of the Brie slices on the tortilla. Add about 6 to 8 of the mango slices, and top with remaining Brie. (This will glue the quesadilla together when cooked.) Top with remaining tortilla and press together.
Heat nonstick 10-inch saute pan and add butter on medium heat. Saute quesadilla until golden brown on both sides. Remove from heat and allow to cool 5 minutes, cut into 8 slices and top with Avocado Salsa.
In a large bowl, mix together all salsa ingredients. Let sit at room temperature for at least 15 minutes to let the flavors mingle.