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Step 1
Preheat oven to 400°F. Grease a 2-quart casserole dish or deep-dish pie plate; set aside (or you can use a 2-quart oven-proof skillet).
Step 2
In a separate bowl, whisk together chicken broth and half-and-half. Set aside.
Step 3
Melt butter in a large skillet over medium-high heat. Add onion, carrot, and celery; sauté for 10 minutes. Add flour and continue cooking and stirring for 1 more minute. Reduce heat to medium and stir in the chicken broth mixture.
Step 4
Continue cooking over medium heat, stirring regularly, until thick (about 5-6 minutes). Make sure that the mixture doesn’t boil. Stir in the salt and pepper. Add chicken and frozen peas.
Step 5
Transfer the mixture to the prepared baking dish (or leave in the oven-safe skillet). Top with the pie crust, sealing and fluting the edges as desired. Cut slits into the top of the crust to allow the steam to escape.
Step 6
Bake in a 400°F oven for about 35-40 minutes, or until the crust is golden brown.
Step 7
Let the pot pie rest for 10-15 minutes before serving.