Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat until hot.
Toss the chopped chicken with 1 tablespoon pesto, then add the chicken to the pan along with the chopped onion, sliced carrots, and quartered zucchini; sauté for about 3 minutes.
Add the chopped red bell pepper, uncooked orzo, and minced garlic; cook and stir for an additional 2 minutes.
Pour in the crushed tomatoes and low-sodium chicken broth, then stir in the remaining 2 tablespoons pesto, optional chicken bouillon, dried oregano, salt, black pepper, and red pepper flakes.
Bring the mixture to a simmer, cover, and reduce heat to medium-low. Simmer 8–12 minutes, stirring every 5 minutes and replacing the lid after each stir, until the orzo and vegetables are tender and the liquid is mostly absorbed.
Stir in 1/2 cup freshly grated Parmesan until melted and combined. Taste and adjust seasoning if needed.
Serve topped with additional grated Parmesan and chopped fresh parsley, if desired.