1/2 freshly grated Parmesan, plus more for serving
1/4 c. freshly grated Pecorino
Preheat oven to 400°. Poke potatoes all over with a fork and place directly on oven racks. Bake until easily pierced with a knife, about 1 hour. Let cool slightly.
When potatoes are cool enough to handle, cut in half and scoop out insides. Discard skins. Run potatoes through a ricer or mash well with a fork.
In a large bowl, combine riced potatoes, flour, eggs, salt, and a little pepper until a dough forms.
Turn dough onto a lightly floured surface and knead until smooth, about 3 minutes.
Divide dough into 4 pieces. Using your hands, roll each piece into a long rope, about ¾” in diameter. Cut ropes into 1” pieces. Place pieces on a lightly floured baking sheet. If dough is too soft to work with this at this point, place in freezer for 10 minutes to chill.
On the back side of a fork, roll each piece along the tines to create ridges and place back on baking sheet.
In a large pot of boiling salted water, cook gnocchi until it floats to the top, about 2 minutes. Reserve 1/2 cup of pasta water, then drain.
Meanwhile, in a large skillet over medium heat, melt butter. Using a slotted spoon, add cooked gnocchi into melted butter. Season with several cranks of black pepper. Add Parmesan and Pecorino and toss until melted and pepper is fragrant, about 2 minutes. Add pasta water, a couple tablespoons at a time to help sauce come together, as needed.