Melt 3/4 teaspoon butter in a large skillet over medium heat, tilting the skillet to evenly spread butter.
Place 1 tortilla in the melted butter.
Cover tortilla with Brie cheese slices and apple slices; sprinkle with brown sugar and cinnamon.
Place the remaining tortilla over the filling.
Cook quesadilla until bottom tortilla is browned, 3 to 5 minutes.
Spread the remaining 3/4 teaspoon butter on top tortilla; carefully flip quesadilla and cook until bottom tortilla is browned and cheese is melted, 3 to 5 more minutes.