Preheat oven to 350 degrees F.
Make sure phyllo is completely defrosted. Once removed from package, you will need to cover phyllo with waxed paper and a damp towel to prevent it from drying out. Lay out sheet of dough, lightly butter with pastry brush. Fold sheet in half, butter again. Keep re-buttering and folding in half (probably 3 "folds" total) until you have a rectangle with dimensions close to 4 by 4 inches. Cut into 3 sections. Sprinkle Parmesan on each piece of dough. Crumble a bit of brie on each. Lay asparagus tip on top and roll dough around asparagus. The tip of the asparagus should show out of the end. Repeat to make 16 pieces. Lay all pieces out on a cookie sheet. Brush each piece with butter and bake in oven until golden brown. Serve warm.