On a clean surface, create a mound of flour with a well in the center. Add eggs, olive oil, and salt into the well. Using a fork, gently mix, incorporating flour without breaking the walls.
Knead the dough for 8-10 minutes until smooth and cohesive. If dry, add a sprinkle of water; if sticky, add more flour. Shape into a ball, wrap in plastic, and rest for 30 minutes at room temperature.
Prepare floured baking sheets. Divide dough into four, flatten one piece, and roll through a pasta machine starting at the widest setting, gradually reducing the setting with each pass until the desired thickness is reached.
Flour both sides of the pasta sheet, fold, and cut into noodles using a pasta cutter. Repeat with remaining dough. Cook in boiling salted water for 1-2 minutes until al dente.