Preheat oven to 375°F (190°C).
Prepare the pie crust in a 9-inch pie dish (store-bought or homemade).
In a skillet, melt butter over medium heat. Add onion, bell pepper, celery, and garlic. Sauté for 5-7 minutes.
Sprinkle flour over the veggies, stir, and cook for 1-2 minutes.
Gradually add chicken broth, stirring until thickened (3-4 minutes).
Stir in heavy cream, Cajun seasoning, salt, and pepper. Cook for 2-3 minutes until smooth.
Fold in crawfish tails and cook for 2-3 minutes to heat through.
Transfer the mixture into the pie crust. Top with another crust and seal the edges.
Brush the top crust with a beaten egg.
Bake for 30-35 minutes, until golden brown and bubbling.
Let the pie cool for 10 minutes before serving.