Chicken Primavera

Name: Chicken Primavera
Ingredients: 3 cloves garlic; 1 pound zucchini (2 small or 1 large); 1 pound asparagus; 1 cup frozen peas; 4 medium boneless, skinless chicken breasts (2 to 2 1/2 pounds total); 2 teaspoons kosher salt, divided; 1 teaspoon freshly ground black pepper, divided; 2 tablespoons olive oil, divided; 1 pint cherry tomatoes; 1 teaspoon dried oregano; 1/4 teaspoon red pepper flakes; 1 cup heavy cream; 3/4 cup low-sodium chicken broth; 5 ounces baby spinach (about 5 packed cups)