1. Place flour on a clean work surface, forming a well in the center. Add eggs to center of well; beat with a fork. Add 1/4 cup olive oil, 1/2 cup water, and salt. Use your hands to slowly mix the flour into the liquid. When dough forms and comes together, lift it out of remaining flour on the work surface using a bench scraper. Sift flour on work surface; set aside. Knead dough for 2 to 3 minutes, adding a little more flour if necessary to prevent sticking.

2. Brush top of dough with remaining teaspoon olive oil to prevent skin from forming, and cover with an inverted bowl. Let rest for 30 minutes.

3. Sprinkle two baking sheets or platters with cornmeal. Divide dough into eight pieces. Lightly flour a work surface with a little of the reserved flour, and roll out or pat one piece of dough into a rectangle about 1/4 inch thick. Cut dough crosswise into 1/2-inch-wide strips. Transfer dough to a clean surface, and using your hands, roll each strip into a strand of spaghetti. Place on prepared baking sheets or platters. Repeat with remaining dough.

4. Bring a large pot of water to a boil; add salt. Cook pasta until al dente, 4 to 5 minutes. Drain, and toss with 2 tablespoons cheese. Stir parsley and basil into sauce. Add pasta to sauce, and gently toss to coat. Sprinkle with 2 tablespoons cheese.