Prepare the Dough: In a large bowl, combine flour and salt. Cut in cold butter until mixture resembles coarse crumbs. Mix egg, cold water, and vinegar; gradually add to flour mixture, kneading until a smooth dough forms. Wrap dough in plastic wrap and refrigerate for at least 30 minutes.
Prepare the Filling: Heat olive oil in a skillet over medium heat. Sauté onions, garlic, and bell pepper until softened. Add ground beef, breaking it up with a spoon. Cook until browned. Stir in tomato paste, smoked paprika, cumin, chili powder, salt, and pepper. Cook 2–3 minutes more. Remove from heat and stir in chopped hard-boiled egg, if using. Let cool slightly.
Assemble the Empanadas: Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper. Roll dough into a ¼-inch thick sheet; cut into 4–5 inch circles. Spoon 1–2 tablespoons of beef filling onto each circle. Fold over and press edges with a fork to seal. Brush empanadas with beaten egg for a golden finish.
Bake: Bake for 20–25 minutes until golden brown. Remove from oven and let cool slightly before serving.
Prepare Chimichurri Sauce: In a bowl, combine parsley, cilantro, garlic, red wine vinegar, olive oil, red pepper flakes, salt, and black pepper. Stir well. Let sit 10–15 minutes to allow flavors to meld. Serve alongside empanadas.