Bring a large pot of lightly salted water to a boil. Add pasta and cook, stirring occasionally, until tender yet firm to the bite, 10 to 11 minutes. Drain and set aside.

Meanwhile, heat olive oil in a large skillet over medium heat. Add squash and sauté until fork-tender, 10 to 15 minutes. Add garlic, sage, and thyme; cook until fragrant, about 1 minute.

Fold in cream and spinach; bring to a simmer. Add 1/4 cup Parmesan cheese and season with salt and pepper.

Add ziti and toss until evenly coated. Cook until sauce has thickened, 1 to 3 minutes. Remove from heat.

Divide between 8 bowls. Top with walnuts and more Parmesan.