How to Make It
Preheat the oven to 375°. Spread 1 1/2 cups of the salt on a baking sheet. Set all the potatoes on the salt and bake for 1 hour, or until tender. Let cool.
Peel all of the baked potatoes. Work them through a ricer into a large bowl. Mix in the remaining 2 tablespoons of salt, the egg yolks and 1 1/2 cups of the flour. Turn the dough out onto a lightly floured work surface and knead it gently 3 or 4 times; add more flour if necessary to keep the dough from sticking. Cut the dough into 6 pieces and cover with a barely damp kitchen towel.
Bring a large pot of water to a boil. Prepare a large bowl of ice water. Working with 1 piece at a time, roll the gnocchi dough on a lightly floured work surface into a 3/4-inch-thick rope. Cut the rope into 1/2-inch lengths. Using your thumb, roll each piece along the back of the tines of a fork to make indentations. Transfer the gnocchi to a lightly floured baking sheet.
Salt the boiling water. Add one-third of the gnocchi and stir gently until they begin to rise to the surface, then cook until just tender, about 1 minute longer. Using a slotted spoon, transfer the gnocchi to the ice water, then drain well on paper towels. Repeat with the remaining gnocchi. In a large bowl, toss the gnocchi with the olive oil. Spread on 2 baking sheets.
In a very large skillet, melt 2 tablespoons of the butter. Cook the butter over moderate heat until it begins to brown, about 1 minute. Add one-third of the pecans and cook, stirring, until toasted, about 2 minutes. Add one-third of the gnocchi and cook until golden brown and warmed through; transfer to a bowl. Repeat with the remaining butter, pecans and gnocchi in 2 more batches. Serve immediately.