In a large pot, cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a skillet, heat olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables begin to soften.
Add the minced garlic and cubed chicken to the skillet. Cook for about 7-10 minutes until the chicken is cooked through and no longer pink.
Sprinkle the flour over the chicken and vegetable mixture, stirring to combine. Cook for an additional 2 minutes to cook off the raw flour.
Slowly pour in the chicken broth and heavy cream, stirring constantly until the mixture begins to thicken.
Add the frozen peas, salt, pepper, thyme, and rosemary. Stir to combine, cooking for another 3-5 minutes until the peas are heated through.
Fold in the cooked penne pasta, coating it well with the creamy sauce.
Remove from heat and allow to cool slightly before serving.