01 - Set oven to 400°F.
02 - In a large skillet, melt butter over medium heat. Add onion, carrots, and celery; cook for 5 to 6 minutes until softened.
03 - Stir in minced garlic and sauté for 1 minute until fragrant.
04 - Sprinkle flour over vegetables and cook, stirring constantly, for 1 to 2 minutes to form a roux.
05 - Slowly whisk in broth, whole milk, and heavy cream. Bring to a gentle simmer and cook until thickened, about 5 minutes.
06 - Add diced turkey, peas, parsley, thyme, salt, and black pepper. Stir to combine and simmer for 2 to 3 minutes. Remove from heat.
07 - Transfer filling into a 9-inch deep pie dish.
08 - Roll out puff pastry to fit dish. Drape over filling, trim excess, and press edges to seal. Cut small slits in pastry for steam release.
09 - Brush beaten egg over puff pastry surface evenly.
10 - Bake for 30 to 35 minutes until pastry is golden and filling is bubbling.
11 - Let stand for 10 minutes to set before slicing and serving.