Melt butter in a large skillet or Dutch oven over medium heat.
Sauté the onion until translucent, approximately 5 minutes, then add the garlic and cook for 1 minute until fragrant.
Stir in the dry orzo and toast for 2 minutes, stirring frequently to prevent burning.
Pour in the chicken broth, thyme, rosemary, salt, and pepper. Bring the mixture to a boil.
Reduce heat to low, cover, and simmer for 8 to 10 minutes, or until the orzo is tender and most liquid is absorbed.
Stir in the shredded chicken, frozen vegetables, and heavy cream.
Cook for an additional 3 to 5 minutes until the vegetables are heated through and the sauce has thickened to a creamy consistency.
Remove from heat, stir in the Parmesan cheese, and adjust seasoning with additional salt and pepper if desired.