Combine fresh spinach, olive oil, and eggs in a food processor. Pulse until mostly smooth. (You can go as smooth as you would like, I like leaving it a little coarser so that you can see the spinach more obviously in the pasta). You can also chop the spinach by hand, using a sharp knife and chopping it finely before adding it to a bowl with the other 2 ingredients.
In a kitchen-aid or bowl, add flour and spinach mixture. Use the dough hook attachment or hands to begin mixing the dough. You may have to add a little water or flour depending on the tackiness of the dough.
Once the dough comes together, knead with the dough hook for 10 minutes until very smooth. OR place dough on counter and knead by hand for 10 minutes.
Cover with plastic wrap and let rest at room temperature for 15 minutes.
Once the dough has rested, it is time to roll it out into noodles. Begin by cutting the dough into quarters.
Take one fourth of the dough and flatten slightly with the palm of your hand and sprinkle flour generously over the whole of it to coat. Begin feeding the dough through the pasta attachment on your Kitchenaid. I begin with the widest setting and gradually work my way to about a 5 on the attachment. You can also use a well-floured rolling pin to roll dough out thinly.
Once the dough is in long sheets, coat with more flour (stickiness is the enemy when feeding through the pasta attachment). Cut dough sheets in half so that the noodles won't be two feet long.
Feed the pasta sheet through the noodle attachment of your choice or use a sharp knife to cut into noodle strips. Allow to dry by hanging (a clothes drying rack works great!). Or lay in floured nests on a baking sheet and cook immediately in boiling water for 3 minutes.