Preheat the oven to 400 degrees F. Cut the tops off of 6 bell peppers and scoop out the seeds and membranes. Set the peppers in a 9x13 inch baking dish. Chop all the vegetables and chicken.
Place a large sauté pan over medium heat. Add the butter. Once melted, add the chopped onions, carrots, celery, garlic, thyme, and rosemary. Sauté for 3-5 minutes to soften.
Stir in the flour so it coats all the vegetables. Then stir in the chicken, peas, chicken broth, 1 teaspoon salt, and 1/4 teaspoon pepper. Allow the mixture to simmer and thicken for 3-5 minutes. Finally stir in the cream and turn off the heat.
Roll out the two pie crusts. Using a wide glass for measurement, cut out six 4- to 4 1/2-inch circles of pie crust. Save the remnants for later use, or discard.
Spoon the chicken mixture into the bell pepper cups, filling them to the top. Place a pie crust circle over the top of each pepper. Use a fork to crimp the edges of the pie crusts so they adhere to the rim of the peppers.
Cut a small vent in the center of each pie crust top. If desired, you can brush extra cream over each pie crust for color, but this is not necessary. Bake for 30-35 minutes. Serve warm.