stand mixer with pasta attachment or hand-cranked pasta machine
Heat the butter and garlic a large saute pan over medium-high heat. When the garlic is lightly browned, about 1 minute, stir in the spinach, season with salt and pepper and continue cooking until wilted. Transfer the cooked spinach to a colander to drain and cool, about 15 minutes. When cooled, gently squeeze the spinach dry, chop it and put in a medium bowl. Fold in the ricotta. Season well with salt and pepper.
Roll out the pasta: Divide the pasta dough in half, working with one half at a time and keeping the other piece wrapped. Set up a pasta roller attachment on a stand mixer (or secure a hand roller to the side of your work surface). Lightly flour a work surface and roll out your dough until it is thin enough to pass through the pasta roller. Set your roller to the widest setting. Turn on the pasta roller and pass the dough through once. Fold the rolled-out piece of dough over itself, and then pass through the roller again. If the edges begin to fray or the dough gets sticky or damp, lightly dust both sides with flour. Repeat six or seven more times, until the dough is smooth. Adjust the roller to the second widest setting, dust both sides of the dough with flour, and pass it through twice (without folding). Repeat, adjusting to a thinner setting each time and passing through twice, until the dough is thin enough that it is slightly translucent.
Fill the tortellini: Dust a work surface and rimmed baking sheet with semolina flour. Lay out the sheet of fresh pasta on the prepared surface and trim into 3 pieces. Cut the pasta sheets into 2-to 3-inch rounds (for tortellini) or squares (for cappelletti). Lightly dampen the pasta with a mister or brush and spoon a teaspoon-sized mound of filling in the center of each piece of pasta. Fold it in half to create a triangle (for square pasta) or a half-moon (for round pasta). Press firmly to seal the edges and eliminate any air. Grab the folded corners of the pasta and place a finger at the center of the folded side of the pasta. Pull the edges around your finger and press the ends together to seal, creating a little pasta "ring" around your finger. Remove your finger and transfer the finished stuffed pasta to the prepared baking sheet. Repeat with the remaining pieces.
Bring a large pot of generously salted water to a rapid boil while you prepare the sauce.
Melt the butter in a large skillet over medium heat, then turn off the stove while you cook the pasta
Drop the tortellini into the boiling water and stir immediately. Leave the tortellini to cook, stirring occasionally, until tender, about 3 minutes.
Use a spider or slotted spoon to transfer the cooked pasta to the melted butter along with 1/2 cup pasta water. Stir to combine and simmer over medium heat for 1 minute, then add the Parmesan. Add some basil and toss to combine. Serve with additional grated Parmesan, if desired.
Mound the flour in the center of a clean countertop or cutting board. Make a well in the center of the flour 3 to 4 inches wide.
Crack the eggs into the well and add a pinch of salt. Using a fork, break the yolks and begin to beat the eggs as you would if making scrambled eggs.
Continue stirring the eggs with a fork in large circles, slowly incorporating the flour. When the eggs form a thick mass and become difficult to stir, about 3 minutes, fold the loose flour from the edges into the pile with a bench scraper and knead until a smooth dough forms. Discard any excess flour.
Shape the dough into a flat disk, wrap tightly with plastic wrap and set aside to rest for 20 minutes before rolling. If waiting more than 1 hour, refrigerate or freeze the dough. The dough will keep refrigerated for up to 24 hours.
If you don't have semolina, you can use 10 ounces of only "00" or all-purpose flour instead of 7 ounces flour and 3 ounces of semolina flour.