Preheat the oven to 350°. Line a small baking pan with rock salt. Pierce the potatoes with a fork and place on the salt. Bake for about 1 hour and 15 minutes, until tender.
As soon as the potatoes are cool enough to handle, peel them and pass them through a ricer into a bowl. Let the potatoes cool.
Lightly dust a baking sheet with flour. Stir the eggs, the 1 cup of flour and the kosher salt into the riced potatoes. Gently knead a few times to form a dough that just holds together. Divide the dough into 4 equal pieces. On a lightly floured work surface, roll out 1 piece of the dough into a 1/2-inch-thick rope. Cut the rope into 1/2-inch pieces and transfer the gnocchi to the baking sheet. Repeat with the remaining dough. Refrigerate the gnocchi for at least 1 hour and up to 4 hours.
Bring a large pot of salted water to a boil. Fill a large bowl with ice water. Boil the gnocchi just until they rise to the surface of the water, about 1 minute. With a slotted spoon, transfer to the ice water to chill, then drain on paper towels and pat dry. Transfer the gnocchi to a bowl and drizzle with olive oil.
In a large skillet, melt 1 tablespoon of the butter in the 1 tablespoon of oil. Add the onion, cover and cook over moderate heat until translucent, 4 minutes. Add the celery, cover and cook over moderately low heat, stirring, until richly browned, 15 minutes.
In a food processor, mince the pastrami. Add the pastrami to the skillet along with the water and chicken broth and bring to a boil. Simmer over low heat until most of the liquid has evaporated, about 1 hour.
In a nonstick skillet, melt 1 tablespoon of the butter. When the foam subsides, add half of the gnocchi and cook over moderate heat, turning, until browned all over, 5 minutes. Transfer to a bowl and repeat with the remaining 1 tablespoon of butter and gnocchi.
Spoon the sour cream onto 4 plates and top with the gnocchi and pastrami ragù. Garnish with the chives and serve.
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