Prepare the lobsters: Bring a large pot of salted water to a boil. Add the lobsters and cook for about 8-10 minutes. Remove and let cool.

Extract the meat: Once cooled, carefully remove the meat from the shells. Chop the meat into bite-sized pieces and set aside. Reserve the shells for serving.

Make the sauce: In a saucepan, melt butter over medium heat. Add shallot and garlic, sauté until soft. Stir in flour to make a roux, cooking for 1-2 minutes.

Finish the sauce: Gradually whisk in milk, cream, and white wine. Bring to a simmer, then stir in mustard, nutmeg, salt, and pepper. Cook until thickened.

Combine lobster and sauce: Add the chopped lobster meat, parsley, and tarragon to the sauce. Stir gently to combine and heat through.

Broil the dish: Spoon the mixture back into the reserved lobster shells. Sprinkle with Gruyère and Parmesan cheese. Broil for 3-5 minutes until golden and bubbly.

Serve immediately: Garnish with additional parsley if desired. Serve hot with crusty bread or a side salad.