Sauté the vegetables. Melt the butter in a large, deep skillet over medium heat. Add the diced onion, carrots, and celery. Cook for 5–6 minutes, stirring occasionally, until the vegetables begin to soften.
Add the seasonings. Stir in the garlic powder, thyme, rosemary, chicken bouillon, salt, paprika, adobo seasoning, and black pepper. Cook for about 1 minute, stirring frequently, until fragrant.
Make the roux. Sprinkle the flour evenly over the vegetables. Stir continuously for about 1 minute, making sure the vegetables are evenly coated. Cooking the flour briefly removes its raw taste and helps create the creamy sauce.
Add the orzo. Stir the uncooked orzo into the seasoned vegetable mixture.
Pour in the broth. Slowly add the chicken broth while stirring to prevent lumps from forming.
Bring the mixture to a gentle simmer. Cook uncovered for approximately 10 minutes, stirring frequently, especially toward the end of cooking, so the orzo doesn't stick to the bottom.
If the mixture becomes too thick before the pasta is tender, add another splash of chicken broth and continue cooking.
Make it creamy. Reduce the heat and stir in the heavy cream or half-and-half.
Add the chicken. Stir the cooked shredded chicken into the Chicken Pot Pie Orzo and cook for another 2–3 minutes, or until the chicken is completely heated through.
Add the vegetables. Stir in the frozen peas or mixed vegetables and cook for 1–2 minutes, just until tender and heated through.
Taste and adjust the salt, pepper, or other seasonings as needed.
Remove from the heat and allow the orzo to rest for a few minutes. Garnish with chopped fresh parsley and optional Parmesan before serving.