Make a well in the center of the flour and add the eggs and oil. Use a fork to mix the eggs, trying not to mix in too much flour.
Use your hands to slowly mix in the flour until it comes together into a shaggy ball.
Turn the dough out onto a work surface and knead the dough for 8-10 minutes. It might seem dry at first, but it will come together. If it hasn't started to come together after 5-6 minutes, wet your hands and keep kneading. Form the dough into a ball and put it back into the bowl, covered with a clean, damp kitchen towel, for 30 minutes.
Divide the dough into four pieces. Working with one piece at a time, flatten it slightly with the palm of your hand and then run it through the widest setting on your pasta machine. Fold the dough so that it resembles a rectangular package then run it through again at the widest setting. Continue to run it through, narrowing the opening, until it is just thin enough to see through. Setting #7 is usually right. Repeat with the remaining dough.
Lay one rectangular piece of dough on your work surface. Spoon or pipe about 1 teaspoon of your filling in dots on top of your pasta and then lay another piece of dough on top. Press gently around the filling to remove any air pockets and seal the pasta.
Cut the pasta out using a stamp, roller, or cookie cutter.
To cook the pasta, bring a large pot of salted water to a boil. Add the ravioli and cook for 2-3 minutes. Once they float to the top they are done. Drain the pasta and toss with olive oil or sauce.