Preheat oven to 375ºF.

Melt butter in a large pot over medium-high heat. Add onion, carrot, and celery and cook for about 3 minutes until the onion turns translucent.

Stir in the chicken or turkey. Sprinkle flour over the mixture and stir to coat. Cook for 1 minute.

Add chicken broth (and wine, if using). Stir and let the mixture cook until it thickens. Add turmeric, salt, pepper, and thyme.

Pour in the half-and-half or cream. Let the mixture bubble and thicken for about 3 minutes. Add more broth if needed. Remove from heat.

Transfer filling to a 2-quart baking dish. Lay the pie crust over the top and press edges to seal. Cut vents in the crust.

Mix egg with 2 tbsp water and brush over the crust.

Place the dish on a baking sheet and bake for 25–30 minutes or until the crust is golden and the filling is bubbly.

Let cool for a few minutes before serving.