Garlicky Pasta Primavera

Ingredients

• 1 cup grated Parmesan cheese, plus more for serving
• 2 Tablespoons minced fresh garlic
• 1/4 teaspoon crushed red pepper flakes
• 2 medium zucchini, cut into 1/2-inch-thick half-moons
• Chopped fresh chives, for serving
• 2 Tablespoons fresh lemon juice, plus more for serving
• 8 oz. asparagus, cut into 1-inch pieces
• 1 teaspoon lemon zest
• 1/4 cup extra-virgin olive oil, divided
• 12 oz. uncooked pasta, such as shells, bowtie or elbow
• 1 cup fresh or frozen peas