Make the pasta by hand: On a clean surface, make a well with the flour. Place 2 of the eggs, 3 tablespoons water, the oil, and salt into a small bowl and stir together with a fork. Pour the wet mixture slowly into the flour and mix with 2 fingers until all of the wet is incorporated. Do not force the dough to take all of the flour. When the dough comes together, knead until smooth, 3 to 4 minutes. Form the dough into a disk and cover with plastic wrap. Place in the refrigerator for 1 hour to rest.
Make the pasta in a food processor: combine the flour and salt in the bowl of your food processor and pulse 2 to 3 times. Whisk together 2 of the eggs, 3 tablespoons water, and the oil in a liquid measuring cup (preferably with a spout). While pulsing the machine, pour this mixture in a continuous stream and continue running the machine until the dough begins to pull away from the sides of the bowl. Form the dough into a disk and cover with plastic wrap. Place in the refrigerator for 1 hour to rest.
Have the pasta rolling machine set to its widest setting. Divide the dough in half, re-wrap, and return one half to the refrigerator. Shape the half you’re working with into an oblong about 5 inches by 2 inches and flatten with your hand until it will fit through the machine. Lightly flour the machine and the dough as you work. Pass the dough through the machine. Fold into thirds as you would a wallet, turn 90 degrees, and pass through the machine again on the same setting. Repeat the folding in thirds, turning 90 degrees, and pass through the machine one last time at the widest setting. Turn the knob to the next size down and pass the dough through. Pass the dough through the machine once on each setting until you get to #6 on the dial. You will have a very long sheet of pasta, approximately 3 feet long.
Take a yardstick and mark the sheet lengthwise down the middle. Do not press so hard that you split the sheet in half. Using a teaspoon measure, spoon about 1/4 ounce of the Italian sausage or meatloaf, or a teaspoon of Spinach Ricotta filling every 2 inches along one side of the mark down the middle — you're looking for 1 inch of dough surrounding each deposit of filling. In a small bowl, whick together the remaining egg and 1 tablespoon of water. Brush the pasta sheet with egg wash on one edge, length-wise, down the entire sheet and in between the filling. Fold the unwashed side of the sheet over and seal, removing any air bubbles as you go.
Using a pizza wheel, cut even squares between each mound of filling. Place the finished ravioli on a parchment paper-lined half-sheet pan and cover with a damp towel. Repeat the procedure with the remaining dough half. You may freeze the pasta on a half-sheet pan lined with parchment paper prior to cooking and once solid, transfer to a zip-top bag for long-term storage. Cook as below when ready to serve.
Fill an 8-quart pot 2/3 full with water, set over high heat, and bring to a boil.
Add the ravioli to the boiling water, 6 to 8 at a time. Cook until they float, 6 to 8 minutes. Remove with a spider and set on a half-sheet pan lined with parchment. Repeat until all the ravioli have been cooked.
Place a 12-inch sauté pan over medium heat and add 2 tablespoons of the butter. When the butter starts to brown, carefully add about 10 ravioli and toss until coated. Sprinkle in the sage and toss again to evenly distribute. Transfer to a serving platter and repeat until all of the pasta has been cooked. Serve immediately.