Place fillets in a single layer on a lightly greased or pan sprayed, shallow oven-to-table type broiler pan. Brush with lemon juice.
In a small bowl, combine remaining ingredients to make the cheese topping mixture. Set aside.
Broil fillets 4 to 6 minutes or until fish flakes easily when tested with a fork. (Time will depend on the thickness of the fillets and temperature of your oven/broiler.).
Remove fillets from oven. Spread with Parmesan topping.
Broil an additional 30 seconds or until cheese is lightly browned and bubbly (be careful to watch it, or it can burn).
Garnish with lemon twists and parsley, if desired.
Note: Mushy cooked fish is a result of either 1) overcooking/overheating, or 2) over-marinating (which, science-wise, is another method of partial cooking, depending on the marinade). Since the flounder in the recipe is not marinated, if the fish comes out mushy I suspect the results are the from overcooking. Either the fish was left under the broiler for too long, the temperature of the broiler is too high, or the rack on which the the pan placed under the broiler is too close to the heat.