Bring the stock to a simmer and add the carrots. Cook for 5 minutes. Add the celery and peas and cook another 3-4 minutes. Drain the vegetables, reserving the broth.
Melt the butter and sprinkle in the flour, using a whisk. Cook over low heat 2-3 minutes, then slowly whisk in the reserved broth, stirring constantly. Raise the heat a bit and bring to a simmer, stirring, and cook 4-5 minutes. Add the cream and cook another 5 minutes to thicken. Stir in the herbs and add the chicken and vegetables and mix.
Pour the creamed chicken into a 9x13 pan (or reserve half and freeze for another day like I did). Top with a pie crust or biscuits, making sure to leave some vents. Cook at 400 for 25-30 minutes (or slightly less if using biscuits as they cook faster).