Preheat oven to 400 degrees F. If desired, remove rind from Brie. Cut Brie into 1/4-inch slices. Brush one side of each tortilla with melted butter. Place tortillas, buttered sides down, on a large baking sheet. Place some of the Brie on half of each tortilla. Top with apples and walnuts. Sprinkle with brown sugar. Fold the other half of each tortilla over apple-nut mixture.
Bake for 8 to 10 minutes or until golden and Brie is melted. Transfer quesadillas to a serving platter or dessert plates. Drizzle caramel topping over quesadillas.