Preheat the oven or air fryer to 375. Prick holes in the potatoes to allow steam to release and drizzle with olive oil and salt. Bake, flipping halfway through, until easily pierced with a knife, 40 minutes to 1 hour. Remove and slice open to allow them to cool.
Once potatoes have fully cooled, scoop out the insides and press through a ricer or gently mash. Fold in egg yolks, 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Pour potato mixture out onto a floured work surface. Dust with 1 cup of flour and begin incorporating flour using a bench scraper to cut and fold the dough. Add more flour in 1/4 cup increments as needed until the dough is no longer sticking to your hands and work surface, but is not dry or crumbling apart. You can knead lightly towards the end to fully incorporate flour.
Line a sheet pan with parchment. Divide the dough into 8 even pieces and roll out each piece into a rope about the thickness of your finger. Cut into one inch pieces. At this point you can use a pasta board or fork and roll each gnocchi against it to create ridges that will better hold a sauce, but this is not necessary. Place gnocchi on parchment paper until ready to boil.
Oil another sheet pan. Boil salted water over medium high heat. Cook gnocchi in batches (about 4 batches) just until they rise to the surface, 3 minutes. Remove with a slotted spoon or strainer basket and place on the oiled sheet pan. Drizzle with more olive oil and toss to coat. Repeat with remaining gnocchi. Toss in your favorite sauce and serve.