Heat oven to 400°. If making a double-crust pie, prep a pie dish with pastry on the bottom. If using only a top crust, butter the bottom of your pie dish, casserole dish, or ramekins. Set aside.

In a large saucepan or dutch oven, heat the olive oil over medium-low heat. Add carrots, celery, onion, and potato and cook gently for about 7 minutes, until vegetables begin to soften but not brown. Add diced chicken and sprinkle the flour over the mixture. Stir to combine and, if using all-purpose flour, cook for 2-3 minutes more.

Gently stir in chicken broth, turn the heat up to medium, and cook for a few minutes, stirring occasionally, until the sauce begins to bubble and thicken. Remove from heat and stir in seasonings and half and half.

Return to low heat and cook gently about five more minutes, until the mixture is heated throughout and nicely thickened but still pourable. Taste and adjust seasonings if needed.

Pour mixture into prepared dish(es) and top with pastry, crimping edges to make it pretty. Slice small holes in top of crust to allow steam to escape.

(If you want to freeze your pie at this point for baking later, first bring it to room temperature, then wrap tightly with plastic wrap and foil before placing in freezer. Defrost for about 30 minutes prior to baking.)

Place your dish(es) on a foil-rimmed baking sheet to catch any drips and bake at 400° for 30-40 minutes (may be less for individual ramekins; start checking for browning at 25 mins). Crust should be golden brown and filling bubbly. Let rest for 5-10 minutes before serving.