Preheat the oven to 375°F (190°C). Place the potatoes on a parchment-lined baking sheet and bake for about 60 minutes, until tender when pierced.
Let the potatoes cool at room temperature for 15 to 20 minutes, then peel them.
Press the peeled potatoes through a food mill or ricer into a large bowl so there are no lumps.
Add the whisked eggs, flour, and sea salt to the mashed potatoes and gently combine until a dough forms.
Turn the dough onto a lightly floured surface and knead briefly for 1 to 2 minutes; add an extra teaspoon or two of flour only if the dough is too sticky.
Divide the dough and roll each piece into a rope about 1/2 inch in diameter.
Cut the ropes into 3/4-inch pieces with a bench knife or knife.
Roll each piece over a gnocchi board or press with the back of a fork to create ridges.
Let the formed gnocchi rest at room temperature for 15 to 20 minutes before cooking or storing.
Bring a large pot of salted water to a boil. Add the gnocchi and cook until they float, about 2 to 4 minutes.
While the gnocchi cook, heat 2 tablespoons unsalted butter or olive oil in a large sauté pan over medium-high heat until shimmering.
When the gnocchi float, drain them and transfer to the hot pan. Sauté for 2 to 3 minutes until lightly browned, then serve.