Directions:

For the gnocchi:

TIP
Gnocchi can be made through this step up to 1 month ahead. To store, place on a flat surface and freeze until frozen through. Transfer to an airtight container and keep frozen up to 1 month before using.

Heat an oven to 425°F and arrange a rack in the middle. Drizzle potatoes with olive oil, season with a few good pinches of salt and a few cranks of pepper, place on a rimmed baking sheet, cut-side down, and roast until fork tender, about 30 minutes.

Set aside until cool enough to handle. Scoop flesh out of skins then pass flesh through a potato ricer (or mash with back of a fork) and stir in cheese, egg, honey, and sat. Mix in flour, about 1/2 cup at a time, until soft dough forms. Taste and add additional salt, as needed. You’ve added flour when you touch the back of the dough and it is damp but not sticking to you hand.

Turn dough out onto floured surface and shape into a square. Divide into 16 equal pieces. Rolling between palms and floured work surface, form each piece into a rope (about 1/2 inch in diameter), sprinkling with flour as needed if sticky. However, don’t add too much additional flour as too much will make for heavy gnocchi. Cut each rope into 1/2 -inch pieces. Stop here or, as desired, use your thumb, roll each piece down over tines of a fork to indent.

Bring large pot of heavily salted water to a slow boil over medium-high heat. Working in batches, simmer gnocchi until tender, about 5 minutes. Using a slotted spoon or spider, transfer gnocchi to clean rimmed baking sheet. Reserve 1/2 cups of pasta cooking water and drain the rest.

TIP
The gnocchi can be made 4 hours ahead — let stand at room temperature then dip in simmering water until heated through.

For the sauce:
This is enough sauce for half of the gnocchi. If you want to cook off all the gnocchi, go ahead and double the recipe. Just a note that I’d recommend you make this sauce through twice as doing twice this amount in one pan would be unwieldy.

Meanwhile, in a large frying pan, melt the butter over medium heat. Once it foams, add sage and cook until crisp and fragrant. Remove sage to a plate and return frying pan to stove. Add shallot and, watching it carefully and stirring often, allow the milk solids begin to brown and the butter becomes fragrant and nutty. Scrape along the bottom to prevent the solids from sticking and burning.

When the butter is brown, immediately remove from heat, and carefully stir in the vinegar (it may sting your eyes). Stir in pasta and 1/2 cup of the reserved pasta water, return to heat, and cook until just coated in the sauce. Add a lot of freshly ground black pepper, taste for seasoning and finish with additional pasta water, salt, black pepper, the crisp sage, and freshly shaved parmesan.