Preheat the oven to 400 degrees F. Poke the potatoes all over with a fork and place them on a baking sheet. Let them roast in the oven for about an hour until they are fork tender. Make sure to really put your fork all the way through and make sure they are done. Give them more time in the oven if they need it.
Set up a food mill or ricer over a bowl and immediately press the potatoes while they are hot from the oven. (My food mill catches the skins, but if yours doesn’t, peel the skin before ricing the potatoes). Spread the riced potatoes all over a baking sheet and let them cool.
To make the gnocchi dough, mix the riced potatoes with the flour, eggs, and salt, and knead gently until it forms a dough. It will be quite sticky. Divide the gnocchi dough into four even pieces. On a well floured surface, roll each gnocchi quarter into a long rope, then cut little pieces off with a knife or bench scraper. Spread the gnocchi out on a floured sheet pan and refrigerate for one hour.
Bring a big pot of water to a boil, and season it heavily with salt, just like you would a pasta water. Prepare an ice bath as well. Boil the gnocchi for a minute or two, and remove them as soon as they float to the surface.Let them cool off in the ice bath for 15 seconds, then remove them to dry on a towel, then transfer the gnocchi to a bowl and drizzle with the 1 tbsp olive oil. Repeat with the remaining gnocchi dough until it’s all cooked.
Heat up 2 tbsp of butter in a skillet over medium heat, and add the onion and celery. Cook for about 10-15 minutes until translucent and soft. Add the chopped pastrami and bump the heat up to medium high. Cook for 10 more minutes, until the pastrami starts to brown like bacon bits. Taste the mixture to season with salt and pepper to taste. Remove the contents from the pan.
Heat the remaining 2 tbsp of butter over medium to medium high heat, and pan fry the gnocchi for a few minutes on each side, until richly browned. Serve with the pastrami mixture sprinkled on top, and garnish with chives. Enjoy!