Add flour and 1 teaspoon salt to a food processor. Pulse a few times. Whisk 4 eggs and water together in a measuring cup. Turn the mixer on and slowly drizzle in the egg and water mixture. Leave the processor on until a ball of dough forms. Continue to let the processor run for 1-2 minutes.
Take the dough out and knead for 4-5 minutes. Form into a ball and wrap in plastic wrap. Let rest for 1 hour.
While the dough rests. Mix ricotta, 1 egg, 1/2 cup pecorino, parmesan, 3/4 tsp salt, and 3/4 tsp pepper together in a medium bowl. Set aside.
Divide the dough in to 8 portions. Take one portion and re-wrap the others while you work. Set the pasta machine to the widest setting. Use a rolling pin to roll the dough into a rectangle. Feed the pasta through the machine on the widest setting. Fold into thirds and repeat. Send through on the widest setting one more time. With each passing after that go one setting smaller than the last until you get to the smallest setting.
Mix 1 egg with 1 tablespoon of water in a small bowl.
Use your ravioli cutter (I use about a 2-inch round ravioli cutter) to make an outline of each of your ravioli so you know where to put the filling. Do this on half of the pasta sheet. You will fold the dough over itself to incase the ravioli. Spoon a heaping tablespoon of filling where you can see the indentation of the ravioli. Use a pastry brush to wet the edges of the ravioli around the filling. Fold the dough over itself to incase the ravioli. Seal tight and make sure there are no air bubbles. Cut each ravioli. (I like to flour my cutter to make sure they don't stick.) Repeat with remaining dough and filling. Alternatively, you can use a ravioli maker like this one or just cut it with a knife. It will taste the same!
Bring a large pot of water to a rolling boil. Season with salt. It should taste like sea water. Cook the ravioli until they float to the top and the pasta is cooked, about 3-4 minutes.
While the pasta cooks. Add the butter to a large skillet. Turn the heat on medium. Once the butter melts, add black pepper. Add 1/4 cup of pasta water. Simmer for 1 minute. Once the pasta is cooked, use a slotted spoon to transfer to butter and pepper. Add remaining cheese and toss. If needed, add more pasta water. Season to taste with salt and pepper. Garnish with parmesan cheese.