Preheat the oven to 400°F and line a baking sheet with parchment paper. Heat a skillet over medium heat and cook the onion with 2 cloves of minced garlic until softened.
Add the ground beef, cumin, smoked paprika, chili powder, salt, and pepper. Cook until the beef is browned and no longer pink, then remove from heat and let cool slightly.
Place a spoonful of the beef mixture in the center of each empanada wrapper. Fold the wrapper over and crimp the edges to seal. Brush the tops with the beaten egg.
Arrange the empanadas on the baking sheet and bake for 15 to 18 minutes until golden and crisp.
While the empanadas bake, combine the parsley, remaining 2 cloves of minced garlic, olive oil, red wine vinegar, and red pepper flakes in a bowl. Stir well and set aside.
Serve the warm empanadas with the chimichurri on the side for dipping.