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, chopped onion, sliced carrots, and quartered zucchini to the pan.
Sauté for about 3 minutes, stirring occasionally, until the chicken begins to brown and vegetables start to soften.
Add the chopped red bell pepper, uncooked orzo, and minced garlic; cook 2 more minutes, stirring so the orzo toasts slightly.
Pour in the crushed tomatoes, 2 tablespoons pesto, and chicken broth; stir in the chicken bouillon (if using), dried oregano, salt, black pepper, and red pepper flakes.
Bring the mixture to a simmer, then cover and reduce heat to medium-low.
Cook, uncovered briefly to stir every 5 minutes (then re-cover), for 8–12 minutes until the orzo and vegetables are tender, stirring occasionally to prevent sticking.
Stir in 1/2 cup freshly grated Parmesan until melted and incorporated; taste and adjust seasoning with more salt and pepper if desired.
Serve topped with additional Parmesan and chopped fresh parsley, if desired.