Preheat your oven to 450ºF and place the potatoes onto a rimmed baking sheet. Pierce the potatoes a few times with a fork then bake in the oven for 45 minutes or until fork tender, flipping halfway through.
Cut the potatoes in half and allow them to cool until cool enough to handle. Remove the potato flesh from the skins and, using a potato ricer or masher, rice or thoroughly mash the potatoes until smooth. Transfer the potatoes to a large bowl and allow them to cool to room temperature. Lightly beat the egg yolks, drizzle them over the potatoes, and lightly mix. Sprinkle over 1 cup of the flour and season with the salt, pepper, and nutmeg. Mix just until a soft, not too sticky dough comes together, adding more flour if needed. Do not overwork the dough as that will lead to dense gnocchi.
Lightly dust a rimmed baking sheet with flour and divide the dough into four pieces. On a lightly floured work surface, roll each piece into roughly a 2cm thick log. Cut each log into roughly 2cm lengths and transfer them onto the prepared baking sheet and set aside until ready to cook.
For the sauce, melt the butter in a large high sided pan over medium heat. Add the shallot into the pan, season with salt and pepper, and cook until lightly golden brown, about 2 to 3 minutes. Stir in the garlic and cook for 30 seconds before stirring in the tomato paste. Cook for about 2 minutes to further intensify the tomato flavour.
Carefully deglaze the pan with the vodka. Allow the vodka to cook down for about 1 to 2 minutes to allow the alcohol to cook off then turn the heat down to low and stir in the whipping cream. Keep the sauce warm over low heat while you cook the gnocchi.
Set a large pot of water to boil over high heat and season well with salt. Cook the gnocchi in two batches for 3 to 4 minutes each or for about 1 minute after they have floated to the surface. When the gnocchi are cooked, transfer directly into the sauce using a slotted spoon. When all the gnocchi are cooked, gently stir about ¼ cup of the gnocchi cooking liquid into the sauce and finish with the Parmigiano-Reggiano, basil, and a final season of salt and pepper. If the sauce is a little thick, stir in another few tablespoons of cooking liquid.
Serve immediately scattered with more basil and parm.
