Bring a pot of water to a boil and fill a bowl with ice cubes and water. Blanch the basil in the boiling water for 10 seconds, then refresh in the ice water. Drain and chop finely; you should have 1/4 cup. Make a mound of the flour, then make a well in the center. Crack the eggs into the well, pour the milk over, and add the basil. Using a fork, stir the egg mixture slowly into the flour to form a wet dough. Add the grated cheese and, working now with your hands, bring the dough together and knead 8 to 10 minutes to form a smooth dough. Allow to rest 15 minutes covered in plastic wrap.
Set up a pasta rolling machine and cut off a piece of pasta dough the size of a tennis ball. Roll the pasta through the rollers on the widest setting, then fold it by thirds and run it through again on the same setting. Repeat this three times, being careful to add very little flour, as it will dry out the pasta. Run the pasta through the next two thinner settings. It should be quite thick.
Lay the sheet of pasta on a floured cutting board and use a knife to cut crosswise into 1/3-inch strips. Lay the cut noodles on a kitchen towel and cover with another. Roll and cut the remaining pasta the same way.
Bring 6 quarts of water to a boil and add 2 tablespoons of salt. In a 12- to 14-inch saute pan, heat 6 tablespoons of the oil and the garlic over medium heat until the garlic is light golden brown, 2 to 3 minutes. Add the zucchini pieces and cook until just soft, 2 to 3 minutes. Add the pepper flakes, wine, basic tomato sauce and butter, bring to a boil, and cook for 1 minute. Add the shrimp and remove from the heat.
Drop the pasta into the boiling water and cook until tender yet al dente, about 3 minutes. Drain and toss into the pan over high heat. Cook until the shrimp are just cooked through, about a minute, and pasta and sauce have become one.
Add the parsley and toss through with the remaining 4 tablespoons of oil, off the heat. Pour into a heated bowl, top with grated scamorza, then serve with plenty of pepper.