Prepare a medium-high (425°F to 450°F) gas or charcoal grill fire. Brush the zucchini and squash slices with oil and season with salt and pepper.
Bring a large pot of salted water to a boil over high heat.
Grill the zucchini and squash until grill marks form on one side, about 2 minutes. Flip the slices and continue to grill until tender, about 1 to 2 minutes more.
Cook the fettuccine in the boiling water according to package directions until al dente.
Meanwhile, cut the squash on a sharp diagonal into 1/4-inch-thick strips.
Drain the pasta, return it to the pot, and add the squash, Parmigiano, cream, and garlic. Gently toss over low heat until combined. Season to taste with salt and pepper.
Serve with more grated Parmigiano at the table, if you like.
nutrition information (per serving):
15, Fat Calories
140, Saturated Fat
13, Monounsaturated Fat
45, Polyunsaturated Fat
Photo: Scott Phillips