Start with the herb crust. Mix flour, chopped herbs, and salt in a large bowl. Cut in cold butter until the mixture resembles coarse crumbs. Gradually add ice water until the dough just comes together. Divide in half, wrap in plastic, and chill for 30 minutes.

Preheat your oven to 375°F (190°C). While the dough chills, prepare your filling.

In a large skillet, melt butter over medium heat. Add carrots, celery, and onions. Cook until vegetables soften, about 8 minutes. Add garlic and cook for another minute.

Sprinkle flour over the vegetables and stir constantly for 1-2 minutes. Gradually add broth and cream, stirring until mixture thickens.

Add turkey, peas, salt, and pepper. Simmer for 5 minutes, then remove from heat.

Roll out one portion of dough and line a 9-inch pie dish. Pour in the filling. Roll out the second portion and cover the pie. Crimp edges and cut slits in the top.

Brush with beaten egg and bake for 45-50 minutes until golden brown.