Mound the flour in a bowl or on the counter and make a well in the center. Crack in the egg, then add the water, olive oil, and salt.

Mix with a fork until shaggy, then knead by hand for 8 to 10 minutes until the dough is smooth and elastic. Wrap in plastic and rest at room temperature for 30 minutes.

Boil the potatoes in salted water until fork-tender, 15 to 18 minutes. Drain and mash while still hot, then set aside to cool slightly.

Melt 1 tbsp butter in the 20 cm / 8-inch skillet over medium heat. Cook the onion until soft, 4 to 5 minutes, then add the spinach and cook until wilted, 2 to 3 minutes. Let cool, then chop finely if using fresh leaves.

Combine the mashed potato, spinach-onion mixture, quark or ricotta, chives, nutmeg, salt, and pepper. Mix until smooth and firm enough to hold a spoon shape.

Roll the dough on a floured surface to about 2 mm thickness. Cut into rounds with the 8 cm cutter, keeping scraps covered under a damp towel.

Place 1 tsp of filling in the center of each round. Fold into a half-moon, press the edges to seal, dabbing with a little water if the dough feels dry, then crimp with a fork.

Bring the stockpot of salted water to a gentle simmer, not a rolling boil, since a hard boil can split the seams. Cook the schlutzkrapfen in batches so they aren't crowded, 4 to 5 minutes, until they float and are tender.

Meanwhile, melt the 60 g butter in the skillet over medium heat with the sage leaves. Cook until the butter turns golden and the sage crisps, 2 to 3 minutes.

Lift the cooked schlutzkrapfen straight from the pot with a slotted spoon into the skillet, tossing gently to coat in the sage butter.

Plate immediately, spoon over any extra butter from the pan, and finish with grated parmesan.