Pour the flour into a mound onto a clean work surface. Make a large well in the center of the flour, then add the eggs, egg yolks, and salt. Use a fork to beat the eggs together, carefully incorporating the flour into the eggs until a wet dough is formed in the center.
Using a bench scraper, fold in the remaining flour, turning the dough 45 degrees each fold to create a dry and firm dough.
Knead the dough by pressing the heel of your hand down and forward into the dough. Turn the dough 45 degrees, knead, and repeat until the dough develops a smooth, elastic texture. Test the dough by slicing it open with a paring knife and looking for air bubbles. If a lot of air bubbles are present, continue kneading the dough. If the dough feels too dry, wet your hands while kneading to slowly incorporate water (you can also use a spray bottle). If the dough is too wet, add a dusting of flour.
Separate the dough into 3 equal-sized pieces using a bench scraper. Roll two of the pieces back together into a ball and cover with plastic wrap to rest. Add the squid ink to the remaining portion and knead until incorporated.* If the dough becomes too wet, add a dusting of flour. Cover with plastic wrap and let the dough rest for 30 minutes.
While the dough is resting, place a piece of parchment paper onto a baking sheet. Add a light dusting of flour to the parchment paper and set aside.
In a medium mixing bowl, combine the ricotta, crabmeat, salt, and pepper. Set aside.
Once the dough has rested, unwrap the plain dough and cut into 3 pieces with a bench scraper. Cover two of the pieces with plastic wrap and set aside.
Place one section of the pasta dough onto a lightly floured work surface. Roll the dough out into a rectangle ½-inch thick. Pass the dough through the pasta attachment set on its widest setting 3 times.
Fold in the narrow ends of the dough so they meet at the middle, then fold the dough in half where the edges meet. Using a rolling pin, roll the dough out into a rectangle ½-inch thick. Pass the dough through the pasta attachment 3 more times. Fold in the ends of the dough again, then fold in half where the edges meet. Use a rolling pin to press the dough together, then feed through the pasta attachment one more time on its widest setting.
Continue to pass the dough through the pasta attachment, reducing the width by 1 setting each time. Once the pasta dough has reached an appropriate thickness for ravioli (often the second or third smallest setting), place the sheet of pasta onto the parchment paper and cover with plastic wrap or a clean towel to keep the dough from drying out.
Repeat steps 8-10 with remaining plain pasta dough sections, cover, and set aside.
Repeat steps 8-10 with the squid ink pasta dough section, then cut the rectangular sheet of dough into 14-inch segments. This will make the sheets of dough easier to work with. Feed the dough segments through a fettuccini or linguine attachment to create the stripes. One by one, lay the strips of black pasta onto the sheets of plain pasta and gently press them together with a rolling pin.
Feed the sheets of striped pasta through the pasta attachment reducing the width until the dough is thin and nearly translucent (about 1/16th-inch, or second to third smallest setting).
Using a food mold or circular cookie cutter, cut the sheets of pasta dough into circles about 3 inches in diameter. Discard any remaining dough.
To assemble the ravioli, add a spoonful of filling to the center of half of the disks. Use a pastry brush to brush a thin layer of water around the filling, then top with another pasta disk, making sure the stripes are facing the same direction. Firmly press down on the edges to make sure the two disks stay together and remove any air pockets. Keep the ravioli covered with a clean towel or plastic wrap to keep from drying out.
While bringing a large, salted pot of water to a boil, prepare the sage butter sauce.