01 - Bring a large pot of salted water to a rolling boil. Add 12 oz of short pasta and cook according to package directions until al dente. Drain thoroughly and set aside.
02 - Heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium heat. Add the diced onion, celery, and frozen peas and carrots. Sauté for 3 to 4 minutes until the vegetables begin to soften. Stir in the minced garlic and cook for an additional minute until fragrant.
03 - Push the vegetables to one side of the pan. Add 2 tablespoons of unsalted butter to the cleared space and let it melt. Sprinkle 2 tablespoons of all-purpose flour over the melted butter, whisking constantly to form a smooth roux. Cook the roux for 1 to 2 minutes to eliminate the raw flour taste.
04 - Gradually whisk in 2 cups of low-sodium chicken broth, ensuring no lumps form. Pour in 1 cup of whole milk and 1/2 cup of heavy cream. Continue stirring continuously for 4 to 5 minutes until the sauce thickens to a silky, coat-the-back-of-a-spoon consistency.
05 - Fold in 2 cups of cooked diced or shredded chicken, 1/2 cup of grated Parmesan cheese, 1 teaspoon of dried thyme, and 1/2 teaspoon of dried parsley. Season with salt and freshly ground black pepper to taste. Stir gently until the chicken is evenly distributed and the cheese has melted into the sauce.
06 - Add the drained pasta to the skillet and toss gently to coat every strand in the creamy sauce. Allow the entire mixture to heat through for 2 to 3 minutes over low heat, ensuring the flavors meld together.
07 - Serve hot in shallow bowls, optionally garnished with a sprinkle of fresh parsley or an extra dusting of Parmesan cheese.