Steps
1. Bring a pot of salted water to a boil and cook the lobster for 8 minutes until bright red. Remove and cool.
2. Split the lobster in half lengthwise and carefully remove the meat from the claws and tail, chopping it into bite-sized pieces. Reserve the shells.
3. In a skillet, melt butter over medium heat, add shallots and cook until translucent.
4. Add white wine and reduce by half.
5. Stir in heavy cream and Dijon mustard, simmer gently until slightly thickened.
6. Add lobster meat to the sauce, season with salt and pepper.
7. Spoon the lobster mixture back into the lobster shells.
8. Sprinkle Gruyère and Parmesan cheeses evenly on top.
9. Broil in a preheated oven at 450°F (230°C) for 3-5 minutes until golden and bubbly.
10. Garnish with fresh parsley and serve immediately.