Preheat the oven to 375°F (193°C). Put the potatoes on a baking sheet and bake until very soft, about 1 to 1½ hours, depending on the size, turning them once. Remove to a wire rack and let sit until cool enough to handle.
Halve the potatoes lengthwise, scoop out the flesh, and discard the skins. Using a food mill or potato ricer, rice the potatoes into a large bowl.
In a small bowl, whisk together the egg yolks, chives, 1½ teaspoon salt, and the pepper until smooth. Add the egg mixture to the potato mixture and mix until completely combined. Begin adding the flour ¼ cup (30 g) at a time and gently fold into the potatoes using a rubber spatula. Add just enough additional flour to make a stiff dough. Knead the dough gently until smooth but still slightly sticky.
Line a baking sheet with parchment paper and dust with flour. Divide the dough into four equal portions.
Gently roll each piece into a rope 12 inches (30.5 cm) long and about 1 inch (2.5 cm) in diameter, flouring as needed to prevent the dough from sticking to the surface. Place dough ropes on the prepared baking sheet and let rest, uncovered, for 30 minutes.
After the dough has rested, place the ropes on a floured surface. Cut each rope into 1-inch (2.5-cm) pieces with a bench scraper or knife and set aside.
Bring a large pot of salted water to a boil over high heat. Add the gnocchi to the boiling water and cook until they rise to the surface, then cook for 1 minute longer. Drain and, using a large slotted spoon, transfer to a clean baking sheet in a single layer. The gnocchi can be made 1 day in advance and stored on a sheet pan in a single layer and covered with plastic wrap.