Preheat your oven to 200°C.
Bake the potato for 60-75 minutes until tender.
Halve the potato and scoop out the flesh while leaving the shells intact.
Boil the cream, mustard, lemon zest, and lemon juice in a pan.
Whisk in egg yolks, half the parmesan, basil, and seasonings until the sauce thickens.
Stir the diced lobster meat into the thickened sauce.
Increase oven temperature to 225°C.
Spoon the lobster mixture into potato shells and top with remaining parmesan.
Bake the filled shells for 3-4 minutes.
Combine cucumber, parsley, tomatoes, onion, oil, and lemon juice for the salad.
Serve the baked potato halves with a portion of the fresh salad.