Soak zucchini at least 20 minutes in cold water, wash off grit, drain, trim ends, and cut into sticks about 3 inches long and 1/8 inch thick. Pat thoroughly dry.

Fry zucchini in oil about 1/2 inch deep over medium-high heat, in batches if needed, turning from time to time. Fry until light brown, not darker, then drain on a rack or paper towels.

When pasta is nearly ready, pour off frying oil, wipe the pan clean and dry, add 2 tablespoons of butter, and heat to medium. When foam subsides, lower to medium-low and stir in the flour-and-milk mixture a little at a time. Stir constantly about 30 seconds. Add a pinch of salt and the fried zucchini, and cook about 1 minute, turning to coat.

Take off heat and vigorously stir in the remaining butter and the egg yolk.

Toss pasta with the sauce, add both cheeses, toss well, then add basil (or parsley), toss once more, and serve immediately.