Preheat the grill to its highest setting and place lobster shells on a baking tray.
Heat 25g of butter in a pan and fry the shallots for 4 minutes until soft.
Reduce the wine by half, then add stock and reduce again before thickening with cream and mustard.
Fry the mushrooms in the remaining butter for 3 minutes and season with salt and pepper.
Stir mushrooms, lobster meat, parsley, lemon juice, and half the Parmesan into the sauce.
Whisk in egg yolks and cook over low heat for 2 minutes to thicken.
Fill the lobster shells with the mixture and top with breadcrumbs and the remaining Parmesan.
Heat vegetable oil in a deep pan to 190°C.
Fry the potato matchsticks for 6 minutes until golden and drain on paper.
Grill the lobster for 4 minutes until the topping is crisp and golden.
Serve the lobster halves with the matchstick fries.