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Gnocchi:
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Place the potatoes in a pot and cover them by 1 to 2 inches/5 to 5 cm with cold water, salt the water and place the pot over high heat.
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Bring the water to a boil and cook until the potatoes are done, 15 to 20 minutes.
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Test the potatoes for doneness by inserting a sharp, thin-bladed knife into them.
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Drain the potatoes and allow them to cool.
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Peel the potatoes using a paring knife and transfer them to a large bowl.
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Crush them with a masher, being careful not to overwork them.
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Lightly flour a work surface and mound the potatoes in the center of it.
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Sprinkle the flour over the potatoes and gently knead them together.
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Make a well in the center of the potato-flour mound.
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Crack the egg into a small bowl, beat it, and pour it into the well.
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Use a fork to work the egg into the potato-flour mound.
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As soon as it is incorporated, begin using your hands to knead the dough until it is no longer sticky.
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Divide the dough into 6 equal portions.
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Roll out each portion of dough, one by one, into a rope-like length 1/2 inch/1 cm in diameter.
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Re-flour the work surface periodically to keep the dough from sticking.
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Cut each rope into 1-inch/5-cm pieces and roll each piece into a small ball.
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If you would like to create a ridged surface to catch sauces, roll each gnocchi off the back of a fork, pressing gently so the tines make an impression.
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Lobster Sauce:
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Bring a pot of water large enough to hold the lobsters to a boil over high heat.
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Add the lobsters, cover the pot, and cook for 8 to 10 minutes.
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Remove the lobsters from the pot and set aside to cool.
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While the lobsters are cooling, bring a large pot of salted water to a boil over high heat.
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When the lobsters are cool enough to handle, remove the meat from the body and claws.
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Cut the meat into bite-size pieces.
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Add the gnocchi to the boiling salted water and cook until they rise to the surface, about 5 minutes.
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Meanwhile, warm the olive oil in a saute pan deep and wide enough to hold all of the ingredients over medium heat.
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Add the shallot and cook until golden brown, about 3 minutes.
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Add the tomatoes and cook for 2 minutes.
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Add the lobster, red pepper, and wine.
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Cook for 2 minutes, but no longer or the lobster meat will toughen.
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Turn off the heat under both the gnocchi and the lobster sauce.
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Transfer the gnocchi to the saute pan using a slotted spoon.
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Add the parsley, season with salt, and toss.
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Serve family-style from a large serving bowl, or divide among individual bowls.
