Preheat your oven to 400 degrees Fahrenheit.
Melt butter in a large skillet over medium heat.
Sauté onions and carrots until they soften, about seven minutes.
Whisk in the flour to create a golden roux, cooking for two minutes.
Slowly pour in the chicken broth and heavy cream, whisking constantly to avoid lumps.
Simmer the sauce until it thickens enough to coat the back of a spoon.
Stir in the cooked chicken and thawed peas, then remove from heat.
Line a deep-dish pie plate with the bottom crust.
Pour the chicken and vegetable mixture into the pie plate.
Top with the second pie crust, crimp the edges to seal, and cut small slits for steam.
Bake for approximately 45 minutes until the crust is golden brown.