Add your whole, unpeeled potatoes to a large pot of cold water, turn the heat to high and bring them to a boil. Once the water is boiling, turn the heat down and simmer until the potatoes are soft and offer little resistance when poked with a knife. Ensure the potatoes are covered with water the entire time, adding more if needed. This should take about 40 to 55 minutes depending on the size of the potatoes. When tender, remove the potatoes and let them cool enough to be handled.

Line a baking sheet with parchment paper and lightly dust it with flour. Set aside.

Next, peel your potatoes and pass them through a potato ricer into a large bowl. Alternatively, you can mash them thoroughly with a fork or pass them through a tamis.

Add the flour, egg, salt and basil to the bowl and mix together with a serving spoon, a fork or your hands. Once the dough comes together, turn it out onto a flat work surface and gently knead until the dough comes together in a ball. Do not knead too much or overwork the dough; rather, combine until just incorporated. The dough should be quite sticky but manageable.

Using just enough flour to make the dough workable, divide it into fourths and roll each section into “snakes” or ropes that are about 3⁄4 inch (2 cm) in diameter.

Cut each “snake” into small pillows about 1 inch (2.5 cm) long (make them smaller or larger if you desire). If you are using a gnocchi board, gently roll each piece into a ball and, and using your thumb, gently push it down into the board to make grooves. You can also use a fork for this or simply roll the gnocchi in your palms so that there are no sharp corners.

Place the gnocchi on the baking sheet in a single layer and set aside until you are ready to cook them. Make sure that the gnocchi are not touching or piled on top of each other, or they may stick.

In a large sauté pan, add the wine, tomatoes, salt, pepper, thyme, and bay leaf over medium heat. Cover and let cook for about 6-8 minutes until the tomatoes soften and begin to break down. Uncover and add the garlic and cook another 5-10 minutes until the tomatoes can be smashed with little effort.

Next, turn the heat to medium-low and, using a splatter guard, cook for an additional 20-30 minutes to concentrate flavors. Remove the thyme sprigs and bay leaf and transfer the mixture to a blender. Blend until smooth and return to the pan. Continue to cook over medium to medium-low heat until the sauce has thickened a bit more, about 5 minutes.

Bring a large, salted (should taste like the ocean) pot of water to a boil. Stir the water before adding the gnocchi to create a whirlpool and prevent the gnocchi from sticking to the bottom of the pot. Add the gnocchi during the last minute of cooking time for the shrimp (see below for timing).

Once the gnocchi water is boiling, check your sauce for seasoning and adjust. Then add the shrimp to the tomato sauce over medium heat. The shrimp will cook in the sauce and will take about 5 minutes or so. About a minute before they are done, drop the gnocchi into the boiling water. The gnocchi will take about 2-3 minutes to cook. Once the gnocchi float, they are done and ready to remove to the sauce.

Once the shrimp are done, turn the heat on the sauce to low and stir in the butter, 1 tablespoon at a time. Add the drained gnocchi to the sauce to coat, remove from the heat and serve the gnocchi. Garnish with fresh basil.