Add the spinach and all-purpose flour to a food processor and blend until the mixture resembles coarse breadcrumbs with no large spinach pieces remaining. This breaks down the spinach fibers and distributes its moisture and color evenly throughout the flour, which is essential for achieving uniform green color and proper hydration in your pasta dough.
Transfer the spinach-flour mixture to a bowl, add the salt and olive oil, and mix with your hands until a shaggy dough forms. Bring it together into a rough ball, then cover and refrigerate for 15 minutes. This rest period allows the flour to fully hydrate and helps relax the gluten, making the dough easier to roll through the pasta machine without tearing.
Remove the dough from the fridge and cut it into 4 equal pieces. Working with one piece at a time, dust your work surface lightly with flour and flatten the dough into a rough rectangle with your hands. Feed it through your pasta machine set at the widest setting, then fold it in half and roll it through 2-3 times. I like to fold and re-roll a few times at the widest setting because it really helps develop the dough's elasticity and creates a smoother final texture.
Gradually tighten the pasta machine rollers and feed the dough through, working up one setting at a time, until it reaches approximately 2 mm thickness. You should be able to see light through the sheet when held up to a window. This gradual thinning prevents the dough from tearing and ensures even thickness for consistent cooking.
Cut the thin pasta sheet into 5 mm wide noodles using your pasta machine's cutting attachment or by hand with a knife. Lay the cut noodles on a lightly floured surface to dry for at least 10 minutes before cooking. Repeat Steps 3-5 with the remaining three pieces of dough. I find that letting the cut pasta air-dry for a bit prevents it from sticking together and gives you more control when cooking.
Bring a large pot of salted water to a boil. Add the fresh spinach pasta and cook for approximately 5 minutes, or until the noodles float to the surface and are tender but still slightly firm to the bite. Drain immediately and serve with your desired sauce.