Boil salted water in a large pot and cook the lobster tails for 8-10 minutes until bright red. Let them cool before extracting the meat.

In a saucepan, melt butter and sauté shallots until translucent. Add white wine and reduce by half.

Stir in heavy cream, Dijon mustard, and brandy. Whisk in egg yolks until fully combined, then add the Gruyère cheese until melted.

Fold in the chopped lobster meat into the sauce and season with salt and pepper to taste.

Preheat the oven's broiler. Spoon the mixture into shells or a baking dish; sprinkle with extra cheese and paprika.

Broil for 5-7 minutes until golden brown. Serve hot, garnished with fresh parsley.