Mound the flour on a clean work surface and create a well in the center. Crack the eggs into the well, add olive oil and salt. Using a fork, beat the eggs gently, then gradually incorporate the flour from the inner walls of the well until a shaggy dough forms.
Bring the dough together with your hands and knead for 8-10 minutes until smooth and elastic. The dough should be firm but pliable. If it's too sticky, add a little flour; if too dry, wet your hands slightly and continue kneading.
Wrap the dough tightly in plastic wrap or cover with an inverted bowl. Let it rest at room temperature for 30 minutes. This allows the gluten to relax, making it easier to roll out.
Cut the dough into 4 pieces. Working with one piece at a time (keep others covered), flatten it slightly and roll out on a floured surface using a rolling pin. Roll from the center outward, rotating the dough frequently, until it's thin enough to see your hand through (about 2mm thick).
Lightly dust the rolled sheet with flour and loosely fold it over itself a few times. Using a sharp knife, cut into strips of your desired width—thin for angel hair, medium for fettuccine, or wide for pappardelle. Unravel the strips and toss gently with flour to prevent sticking.
Bring a large pot of salted water to a rolling boil. Add the fresh pasta and cook for just 2-4 minutes, stirring occasionally. Fresh pasta cooks much faster than dried! Taste to check for doneness—it should be tender but still have a slight bite.
Reserve a cup of pasta cooking water before draining. Drain the pasta and immediately toss with your favorite sauce. Add a splash of the reserved pasta water if needed to help the sauce coat the noodles. Serve immediately while hot.