In a large skillet over medium heat, brown the ground beef until fully cooked, about 5-7 minutes. Drain excess fat if necessary.

Add the diced onion and minced garlic to the skillet, cooking until the onion is translucent, about 3-4 minutes.

Stir in the mixed vegetables, beef broth, Worcestershire sauce, thyme, salt, and pepper. Bring to a simmer.

Sprinkle the flour over the mixture and stir to combine, cooking for an additional 2 minutes until thickened.

Pour in the milk and stir until the mixture is creamy and heated through. Remove from heat.

Preheat your oven to 400°F.

Roll out the pie crust over the beef mixture in the skillet, tucking the edges down into the sides of the skillet. Cut a few slits in the crust to allow steam to escape.

Brush the top of the crust with the beaten egg for a golden finish.

Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown.

Allow to cool for 5 minutes before serving.