Cook the pasta in plenty of boiling, salted water, stirring occasionally, until al dente, or firm to the bite, 10 to 12 minutes. Before draining, ladle out 1/2 cup of the boiling cooking water and reserve.

Meanwhile, heat the oil in a large skillet over medium heat. Add the scallion and garlic; cook, stirring, for 2 minutes. Add the zucchini and yellow squash and cook, stirring, over medium-low heat just until wilted, about 3 minutes.

Toss the pasta with the zucchini mixture and stir in the basil, mint, reserved cooking water and 1 tablespoon of the cheese. Spoon onto plates, and serve with a light sprinkling of cheese over each serving.