Preheat your oven to 400°F (200°C) and lightly grease a pie dish.

Melt butter in a skillet over medium heat. Add onions and garlic, sautéing until they become translucent, about 3-4 minutes.

Stir in the diced carrots, potatoes, and peas. Cook for 5–7 minutes until they’re slightly tender.

Sprinkle flour over the sautéed vegetables and ham. Stir well to coat everything evenly.

Pour in the milk gradually, stirring constantly until the mixture thickens, about 5 minutes. Season with salt, pepper, paprika, and thyme.

Place one pie crust in the greased dish. Pour the creamy filling over the crust, spreading it out evenly.

Top with the second crust, trimming the edges as necessary. Cut slits for steam to escape and brush with beaten egg.

Bake for 25–30 minutes, or until the crust is golden brown and the filling is bubbling. Let rest for 10 minutes before slicing.