How to Make It
In a food processor, combine the 1 3/4 cups of flour with a pinch of salt. Add the whole egg, 5 of the egg yolks and 1 tablespoon of water and process until a crumbly dough forms, about 2 minutes. Turn the dough out onto a work surface and knead until smooth; if the dough is too tough to knead, add another tablespoon of water. Wrap the dough in plastic and let stand at room temperature for 30 minutes.
Unwrap the dough and divide it into 3 pieces. Work with 1 piece at a time and keep the rest covered. Press the dough to flatten it slightly. Using a hand-cranked pasta machine set at the widest setting, roll the dough through successively narrower settings to the thinnest one. Lay the pasta on a lightly floured work surface, sprinkle with flour and cover with wax paper. Repeat with the remaining dough, dusting with flour and layering between wax paper.
Using a 2 1/4-inch fluted biscuit cutter, stamp out rounds from the pasta sheets. Cover with plastic wrap.
In a bowl, combine the ricotta with 1/3 cup of the Parmigiano-Reggiano, the spinach, oil and nutmeg and season with salt and pepper. Transfer the filling to a pastry bag fitted with a 1/4-inch round tip or to a sturdy plastic bag with a corner snipped off.
In a small bowl, combine the 2 remaining yolks with 1/4 cup of water. Working with one dough round at a time, lightly brush the edge with the egg wash. Pipe a scant 1/2 teaspoon of the filling in the center and fold the dough over the filling to form a half moon; press the edge to seal. Lightly brush the dough with water if dry. Bring the ends of the half moon together around your finger, overlapping them slightly and pressing them together. Fill and shape the remaining tortelli, transferring them to a tray lined with floured wax paper.
Bring a large pot of salted water to a boil. Add the tortelli and cook, stirring occasionally, until they rise to the surface and the pasta is cooked through, 7 to 8 minutes, then drain, reserving 1/4 cup of the water. Transfer the tortelli to a large bowl.
In a large skillet, cook the butter over moderately high heat until lightly browned, 5 minutes. Stir in the tortelli, the reserved pasta water and the remaining 1/4 cup of grated cheese. Serve right away.