In the bowl of a food processor, add the basil leaves and flour. Process until the basil leaves are finely chopped and incorporated.
Add the eggs, flour, and olive oil. Process and slowly add the water as needed just until dough comes together.
On a lightly floured surface, knead the dough until smooth and elastic. Cover and let rest 30 minutes.
Divide the dough into four equal pieces. Place one on floured work surface and cover the remainder.
Roll the dough into a thin sheet using a pasta machine or rolling pin, until it is about 1/16th inch thick. Cut into desired shape. To make farfalle: slice the pasta sheet into 1 1/2 by 1 inch rectangles. Use your thumb and forefinger to pinch the long edges together to form a bow. Repeat with remaining rectangles, then remaining pieces of dough. Arrange the pasta in a single layer on baking sheet or work surface and allow to dry for 1 hour.
Bring a large pot of salted water to a boil. Add the pasta in batches, careful not to overcrowd, and boil until they rise to the surface. Remove to a colander and drain.
Serve immediately with desired sauce.