Preheat your oven to 375 degrees Fahrenheit. Spray a 2-quart casserole dish with cooking spray. See note 1.
Melt the butter in a large skillet or a large soup pot. Add the carrots, onion, celery, and garlic. Season with salt and pepper and sauté until the vegetables are soft, about 5 to 7 minutes.
4 tablespoons unsalted butter, 2 large carrots, 2 celery stalks, 1 small yellow onion, 2 cloves garlic, 1 teaspoon salt, 1/2 teaspoon black pepper
Whisk in the flour. (It will look very gummy, but you are on the right track.) Then slowly whisk in the chicken stock, scraping up any browned bits. While you want to go slowly, this should only take about a minute. Whisk in the milk, thyme, and add in 2 bay leaves. Bring to a simmer.
1/2 cup all purpose flour, 2 1/2 cups chicken broth, 1 cup milk, 1/2 teaspoon dried thyme, 2 bay leaves
Add in the chicken and cook for 10 minutes or until the chicken is cooked through. Discard the bay leaves and stir in frozen peas. Pour into the prepared casserole dish.
1 pound boneless skinless chicken breasts, 1 cup frozen peas
Top the casserole dish with the puff pastry. You can do this as a whole sheet, cutting a few holes to vent. Or you can cut the puff pastry into strips and weave it into a lattice top. See the video for a step by step on how to do this. Then brush the puff pastry with the egg wash.
1 sheet puff pastry, 1 egg
Bake for 25 to 35 minutes or until the puff pastry is golden brown. Allow to cool for 10 minutes before dishing up.