2 lobsters (about 1 1⁄2 lbs. each)
2 cups milk
7 tbsp. unsalted butter
1⁄4 cup flour
1 tsp. ground nutmeg
Freshly ground black pepper, to taste
2 shallots, finely chopped
1⁄2 lb. cremini mushrooms, quartered
1 cup white wine
1 1⁄2 cups heavy cream
1 tbsp. finely chopped chervil
1⁄8 tsp. cayenne
1⁄2 tsp. dry mustard
1⁄2 lb. gruyère, grated
1. Bring a pot of salted water to a boil. Add lobsters; boil for 5 minutes. Drain; halve each lengthwise. Remove and crack claws. Remove meat from bodies and claws; cut into chunks. Scrape shells' insides clean; set meat and shells aside.
2. Bring milk to a boil; set aside. Melt 4 tbsp. of the butter in a pan over medium heat. Add flour and cook until golden, 1–2 minutes. Add milk while whisking; increase heat to medium; boil. Cook, stirring, until thickened, 2–3 minutes. Add nutmeg and salt and pepper; keep sauce warm.
3. Heat broiler. Heat remaining 3 tbsp. of the butter in a skillet over medium-high heat. Add shallots; cook until golden, 1–2 minutes. Add mushrooms; cook until softened, 4–5 minutes. Add wine; cook until reduced by two-thirds, 4–5 minutes. Whisk in cream, chervil, cayenne, and reserved sauce. Reduce heat to medium-low; cook until thickened, 3–4 minutes. Add lobster; stir in mustard and 3⁄4 cup cheese. Divide half of lobster sauce between shells; sprinkle remaining cheese over top. Broil lobster halves on a baking sheet until bubbly, 2–3 minutes. Serve with remaining sauce.