I start by boiling the purple potatoes with their skins on. Once tender, I peel and mash them, preferably using a potato ricer.
Then I add the flour, egg yolk, and salt, gently mixing everything into a soft dough. Do not overwork it.
I roll the dough into long ropes, cut them into small pieces, and shape them using my wooden gnocchi board. A fork or your finger works too.
I cook them in gently boiling salted water until they float, then give them another 30–60 seconds.
For the pesto, blend everything in a food processor, adding olive oil gradually until the desired consistency. Gently toss the gnocchi with fresh pesto, adding a splash of cooking water if needed.