Preheat an oven to 200 degrees F (95 degrees C).

Combine the water with 2 tablespoons salt in a large pot; bring to a boil

Plunge lobster into boiling water, cover the pot, and return the water to a boil. Reduce heat to medium-low and cook at a simmer until the lobster becomes bright right, about 10 minutes.

Remove the lobster from the water and set aside to cool.

When cool enough to handle, clean lobster and pull out tail meat, reserving the tail shell. Crack claws and remove the meat.

Chop the tail meat coarsely and reserve with the intact claw meat in a covered dish; keep warm in the preheated oven.

Put about 1 inch of water in the bottom of a saucepan with 1 teaspoon salt; bring to boil.

Add potatoes to the boiling water; top with intact lobster tail shell.

Cover the saucepan and return the water to a boil. Reduce heat to medium low and cook at a simmer until the potatoes are easily pierced with a fork, 20 to 30 minutes.

Remove lobster shell and discard.

Drain the water from the saucepan.

Reduce the heat to low. Gently shake the pan over low heat to dry the potatoes.

Add the butter to the potatoes and mash until no lumps remain.

Add cream until you get your preferred consistency

Fold in reserved chopped lobster meat.

Sprinkle with paprika to serve.