Add flour, salt, and eggs to a food processor. Pulse until dough forms. Separate dough into 6 pieces. Place dough on a plate, cover with a kitchen towel, and leave in a cool place for 30 minutes.
Run each piece of dough through a pasta roller. Reduce the roller setting (to make the dough thinner) after each pass, until you get to the final setting. {If you don't have a pasta roller, you can roll the dough by hand. Roll it until it's really really thin. If you think it's thin enough, keep rolling, it's probably not. I learned the hard way.}
Drape dough over a clothes rack of something similar {I hung my pasta over the top of my kitchen cabinets} for 10 minutes.
Filling & Assembly:
Bring a large pot of water to a boil. Season water with salt.
In a large bowl, mix together cheeses, basil, oregano, and pepper until well combined.
Using a 2" or 3" round cutter, cut out circles from your rolled pasta dough. Place 1/2 tablespoon filling in the center of half of the pasta circles if using a 2" cutter. (The recipe says to use 2 teaspoons filling for a 3" pasta round.)
Using your finger, rub some water round the edge of the pasta circle with filling until it's well moistened. Top each filled circle with a second pasta circle. Carefully press down, sealing the edges, and removing any air from around the pasta filling. {I went back and pressed any extra air out after I closed all the ravioli.}
Take a fork and gently press down around the entire edge of the ravioli with the fork tines. {This isn't part of the original recipe, but I was paranoid the filling would try to get out.}
Gently drop pasta into water and cook for 3 minutes. Pasta will sink and then float when ready. Give the pasta a little stir while it's cooking to make sure it doesn't stick.
Drain the ravioli. Serve with your favorite sauce and a little extra Parmesan cheese on top!