Instructions

1. In a large bowl whisk together the eggs, egg yolks, parmesan, pecorino, black pepper and a pinch of salt. Set aside.
2. Bring a large pot of water to a boil. Season the water generously with salt. Keep the water at a simmer while you start the zucchini.
3. Quarter the zucchini lengthwise. Using the tip of your knife, remove and discard the seeds. Cut  the zucchini into 1/3 inch pieces. Place a medium Dutch oven over medium high heat. Add the oil to the pan and heat until the oil moves freely, another 30 seconds or so. Add the zucchini, garlic, basil and 1/2 teaspoon salt to the hot pan and stir to combine. Cover the pan and allow the zucchini to cook for 15 minutes, stirring every 3 to 4 minutes to prevent burning. Your goal is to develop a few golden bits in the zucchini while also creating a few broken down pieces.
4. While the zucchini cooks bring the pasta water back to a full boil. Add your pasta to the water to cook.
5. Once the zucchini is broken down and the there are few golden-brown spots sticking to the pan, add 1/4 cup of pasta water to the pan and stir, scraping up the brown bits as you do. Those bits are the flavor.
6. In a steady stream, whisk 1/4 cup of pasta water into the egg mixture. Add the hot zucchini to the egg mixture stirring constantly with a wooden spoon to combine. Both of these steps will help temper the egg mixture. When the pasta is al dente, after about 10 minutes, use tongs to remove the pasta from the cooking water directly to the bowl with the egg and zucchini mixture. Using the tongs start tossing and stirring the pasta to create a silky sauce that clings to the pasta. This will take about 4 minutes. Serve with additional parmesan cheese and black pepper if desired.