In a large mixing bowl, create a mound with the flour and make a well in the center. Add the eggs, salt, and olive oil into the well.
Using a fork, beat the eggs gently, then gradually incorporate the flour from the edges of the well into the eggs. Continue until it forms a rough dough.
Transfer the dough to a lightly floured surface. Knead the dough for about 8-10 minutes until it becomes smooth and elastic. If the dough is too sticky, add a little more flour as needed.
Wrap the dough in plastic wrap and let it rest for at least 20 minutes at room temperature.
Once rested, divide the dough into four equal pieces. Take one piece and keep the others covered to prevent drying.
Roll out the dough using a rolling pin or a pasta machine, to your desired thickness (about 1/16 to ⅛ inch). Dust with flour as necessary to prevent sticking.
Cut the rolled dough into your desired pasta shape using a knife or pasta cutter.
Dust the cut pasta with a little flour to keep it from sticking together. Repeat the process with the remaining dough.
Cook the pasta in a large pot of boiling salted water for about 2 minutes or until it reaches your desired doneness.
Drain the pasta and serve immediately with your favorite sauce.