Combine Wet Ingredients: In the bowl of a stand mixer, add the eggs, olive oil, and salt. Attach the whisk attachment and beat on medium speed until the ingredients are well combined and slightly frothy, about 30 seconds.
Incorporate Flour: Remove the whisk attachment. Add the "00" flour to the wet ingredients in the mixing bowl. Using a sturdy spoon or spatula, stir for about 1 minute until the flour is mostly incorporated and a shaggy dough begins to form.
Knead with Mixer: Switch to the dough hook attachment on your stand mixer. Mix on low speed (setting 2 on most KitchenAid mixers) for 7-10 minutes. Continue mixing until the dough comes together into a cohesive ball that pulls away cleanly from the sides of the bowl. The dough should look smooth and elastic.
Hand Kneading (Optional, but Recommended): Turn the dough out onto a lightly floured clean work surface. Knead by hand for an additional 2-3 minutes until the dough is perfectly smooth and springs back when gently pressed. This ensures optimal texture.
Rest the Dough: Form the dough into a ball and lightly flatten it. Wrap tightly in plastic wrap (or beeswax wrap) to prevent drying. Let the dough rest at room temperature for at least 20 minutes. For a larger batch or if you have more time, you can refrigerate it for 1-2 hours; bring to room temperature before rolling.
Roll and Cut - After resting, divide the dough into 2-4 portions. Working with one portion at a time, flatten it into a disc. Pass the dough through a pasta roller, gradually decreasing the thickness setting until your desired pasta thickness is achieved (typically setting 6 or 7 on most machines for spaghetti/fettuccine). Use a pasta cutter attachment or a sharp knife to cut the sheets into your desired pasta shape (e.g., fettuccine, tagliatelle, lasagna sheets).
Cook Fresh Pasta: Bring a large pot of heavily salted water to a rolling boil. Add the fresh pasta and cook for 2-4 minutes, or until al dente. Fresh pasta cooks much faster than dried pasta, so taste frequently!
Serve: Drain the pasta and toss immediately with your favorite sauce.