Combine the potatoes and 1 teaspoon of salt in a large saucepan over medium heat. Cover the potatoes with water and cook until fork tender, about 20 minutes. Drain. Return, the potatoes to the pan and over low heat, stir them with a fork or wire whisk for about 2 minutes to dehydrate them. Add the cream and garlic pulp. Stir to incorporate well. Mix in the white pepper.
Season the lobster meat with salt, to taste, and set aside. Using a sharp knife, chop 1 lobster shell.
In a saucepan, over medium heat, combine the butter and chopped lobster shells. Melt the butter and simmer over low for about 10 minutes. Remove and strain.
In a saute pan, over medium heat, add 2 tablespoons of the lobster butter. When the butter is hot, add the diced lobster and saute for 2 minutes.
To assemble, form 1 cup of the potatoes into a circle, in the center of each plate. Spoon 1/4 of the lobster of each circle of potatoes. Spoon 1/4 of the butter, or to taste, around each circle of potatoes. Arrange 1/4 of the cheese on top of each plate of lobster. Mound the arugula on top of the cheese. Garnish with parsley.