Cook the Lobster: Boil the lobsters until fully cooked, then remove the meat from the shells and chop it into bite-sized pieces.
Prepare the Sauce: In a saucepan, melt butter, add flour, and cook until golden. Gradually whisk in milk until smooth. Stir in Gruyere and Parmesan cheeses until melted. Add Dijon mustard, salt, and pepper.
Combine Lobster and Sauce: Add lobster meat to the sauce, ensuring an even coating. Spoon the mixture back into the lobster shells.
Broil the Lobsters: Place the filled lobster shells under the broiler until the top is golden and bubbly.
Garnish and Serve: Sprinkle with fresh parsley before serving.