Preheat oven to 375°F (190°C). Place whole potatoes on a parchment-lined baking sheet and bake for about 60 minutes, until completely tender when pierced.
Let the baked potatoes cool 15–20 minutes at room temperature, then peel them while still warm.
Press the peeled potatoes through a food mill or ricer into a large bowl so there are no lumps.
Add the whisked eggs and sea salt to the riced potatoes; gently mix to combine.
Sprinkle the flour over the potato mixture and fold together until a soft dough forms; do not overwork.
Lightly knead the dough on a floured surface 1–2 minutes, adding up to 1–2 teaspoons more flour if the dough is too sticky.
Divide the dough into portions. Roll each portion into a rope about 1/2 inch (1.25 cm) in diameter.
Cut the ropes into 3/4-inch (2 cm) pieces with a bench knife, then shape each piece by rolling it down a gnocchi board or pressing with the back of a fork to create ridges.
Let the formed gnocchi rest at room temperature 15–20 minutes before cooking or storing.
Bring a large pot of salted water to a boil. Add gnocchi in batches and cook until they float, about 2–4 minutes.
While gnocchi cook, heat 2 tablespoons unsalted butter or olive oil in a large sauté pan over medium-high heat until shimmering.
When gnocchi float, drain them and transfer to the hot sauté pan; brown for 2–3 minutes until lightly golden, then serve.
