Preheat the grill to its highest setting. Place the lobster shells onto a large baking tray and set aside.
Heat half of the butter in a frying pan over a medium heat until foaming. Fry the shallots for 3-4 minutes, until softened.
Pour in the wine and bring the mixture to the boil. Simmer until the volume of liquid has reduced by half, then add the stock and continue to simmer until reduced slightly. Add the double cream and mustard and simmer again for 3-4 minutes, until slightly thickened.
Meanwhile, heat the remaining butter in a separate frying pan over a medium heat. Add the mushrooms and fry for 2-3 minutes, until just softened. Transfer to a bowl and season well with salt and pepper.
When the sauce has reduced, add the mushrooms and lobster meat and stir through. Add the parsley, lemon juice and half of the Parmesan and season again.
Whisk in the egg yolks and continue to cook the mixture over a low heat for 1-2 minutes, until just thickened.
Divide the lobster meat and sauce between the lobster shells, then sprinkle over the breadcrumbs and remaining Parmesan.
Meanwhile, heat the vegetable oil in a deep-fat fryer to 190C. Alternatively, heat the oil in a heavy-based, deep-sided pan until a breadcrumb sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous; do no leave unattended.)
Carefully lower the chipped potatoes into the hot oil and fry for 4-6 minutes, or until tender and golden-brown. Remove and drain on kitchen paper.
Meanwhile, grill the lobster thermidor for 3-4 minutes, or until the topping is crisp and golden-brown.
Serve the lobster halves on plates with a pile of matchstick fries alongside.