Begin by cooking 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 diced onion and cook until translucent, about 3-4 minutes.
Add the minced garlic, diced carrots, and celery to the skillet, sautéing for another 5-6 minutes until the vegetables are tender.
Stir in the shredded chicken and frozen peas. Mix well to combine.
Pour in the chicken broth and heavy cream, stirring until everything is well incorporated.
Add the dried thyme, dried rosemary, salt, and pepper. Bring the mixture to a simmer, cooking for about 10 minutes until the sauce thickens slightly.
Add the cooked penne pasta to the skillet, mixing everything together to coat the pasta with the sauce.
If desired, sprinkle the grated Parmesan cheese over the top and stir until melted.
Serve hot in bowls and enjoy your Chicken Pot Pie Pasta.