Place basil in a food processor; cover and process until finely chopped.
Add flour and process until blended.
Add in the eggs, water and oil. Process for 15-20 seconds or until dough forms a ball.
Turn onto a floured surface and knead until smooth and elastic (about 8-10 minutes).
Cover and let rest for 30 minutes. Then divide into fourths.
On a floured surface, roll each portion of dough to 1/16-in. thickness.
Roll up jelly-roll style and cut into 1/4-in. slices.
Separate and unroll the slices.
Hang to dry or let stand on a clean towel for 1 hour.
Cook noodles in boiling salted water for 4-5 minutes or until tender; drain.