Shave the zucchini into long ribbons with a vegetable peeler, discarding the seedy core.

Crisp the pancetta in a skillet with the olive oil over medium heat until golden, 5 to 7 minutes. Remove the pancetta, keeping a little fat in the pan.

Whisk the egg yolks, both cheeses, and plenty of black pepper in a bowl until thick and smooth.

Cook the spaghetti in salted boiling water until al dente. In the last 30 seconds, add the zucchini ribbons. Drain, reserving 1 cup pasta water.

Off the heat, toss the hot pasta, zucchini, and pancetta with the egg mixture, drizzling in a splash of pasta water at a time until the sauce is silky. Serve right away with extra cheese.