Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced carrots, celery, and shredded chicken to the skillet. Cook for about 5 minutes until the vegetables start to soften.
Sprinkle the flour over the chicken and vegetables, stirring to coat and cook for an additional 2 minutes.
Gradually pour in the chicken broth while continuously stirring to avoid lumps. Add the thyme, rosemary, and season with salt and pepper.
Bring the mixture to a simmer and let it thicken for about 5 minutes.
Once thickened, reduce the heat and stir in the heavy cream, followed by the frozen peas. Allow everything to cook for another 2-3 minutes until heated through.
Add the cooked penne pasta to the skillet, mixing it in with the sauce until the pasta is well coated.
Adjust seasoning if necessary, and serve hot, garnished with freshly chopped parsley.