Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook until softened, about 3-4 minutes. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks. Drain any excess fat.

Stir in the minced garlic and cook for 1 minute until fragrant. Add the diced potatoes and frozen vegetables, then sprinkle with flour. Stir well to coat everything evenly. Pour in the beef broth and Worcestershire sauce, then add thyme, paprika, salt, and pepper. Bring to a simmer, then reduce heat and cook for 10-12 minutes until potatoes are tender and sauce has thickened.

Preheat oven to 375°F (190°C). Place one pie crust in a 9-inch pie dish. Spoon the beef and potato filling into the crust, spreading it evenly. Place the second crust over the filling, seal the edges, and crimp with a fork. Cut several slits in the top crust to allow steam to escape. Brush the top with beaten egg for a golden finish.

Bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbling. Let the pie rest for 10 minutes before slicing and serving. This resting time allows the filling to set perfectly.