Add the garlic to a food processor and pulse until finely minced. Add the feta, ricotta, grated hard cheese, egg, egg yolk, lemon zest, nutmeg, salt, and parsley. Pulse briefly until combined; the mixture should still have some texture.

Transfer the mixture to a mixing bowl. Gently fold in the all-purpose flour and semolina flour until just combined. The dough will be soft and sticky.

Dust a sheet pan generously with semolina flour. Spoon the dough onto the pan and gently shape it into a rectangle about 7 by 9 inches and just over ½ inch thick. Sprinkle the top with more semolina, cover loosely, and refrigerate for at least 2 hours or until firm.

Once chilled, cut the dough lengthwise into 8 strips. Slice each strip into 4 pieces, then cut each piece diagonally to create triangles. Lightly toss the dumplings in semolina flour so they are coated on all sides.

Bring a large pot of well-salted water to a gentle, barely bubbling heat. Carefully add the dumplings one at a time. Cook for about 15–16 minutes, keeping the water calm. Remove with a slotted spoon and let them rest briefly on a paper towel–lined tray.

Heat the olive oil in a wide skillet over medium heat. Add the pine nuts and Fresno peppers and cook for 1–2 minutes, stirring, until the nuts are lightly golden. Stir in the grated garlic and cook for another 2–3 minutes until fragrant. Season lightly with salt.

Lower the heat and stir in the chopped dill and the vinegar–lemon mixture. Add the cooked dumplings to the skillet and gently toss to coat. If needed, add a small splash of the cooking water to loosen the sauce.

Serve warm with extra grated cheese on top.