Heat the olive oil in a large skillet over medium-high heat. Add the ground beef, kosher salt, and black pepper. Break the beef into small pieces and cook for 3 to 4 minutes. Add the diced onion when the beef is almost browned and continue cooking for another 3 to 4 minutes, stirring occasionally, until the beef is cooked through and the onion has softened. Drain any excess fat, leaving no more than a light coating in the skillet.

Add the diced roasted red peppers and cook for about 2 minutes, stirring occasionally, until the excess moisture has evaporated. Stir in the minced garlic and cook for 30 seconds, until fragrant.

Add the tomato paste, smoked paprika, dried oregano, and cayenne pepper. Cook for 1 to 2 minutes, stirring constantly, until the tomato paste darkens slightly and coats the beef and vegetables. Remove the skillet from the burner and stir in the red wine vinegar, chopped green olives, and fresh parsley. Taste and adjust the seasoning if needed. Set the filling aside to cool while preparing the aioli.

Whisk together the mayonnaise, smoked paprika, minced garlic, fresh lemon juice, and kosher salt in a small bowl until smooth and thoroughly combined. Cover and refrigerate until ready to serve.

Preheat the oven to 400°F (200°C). Line two large baking sheets with parchment paper. Arrange the eight thawed empanada pastry discs on a work surface.

Divide the cooled beef filling evenly among the eight pastry discs, placing the filling on the lower half of each disc and leaving an uncovered border around the outside. Fold the empty half of the pastry over the filling to form a half-moon. Gently press out any trapped air, press the pastry edges together firmly, and crimp with the tines of a fork to seal.

Transfer the baked empanadas to a wire cooling rack and allow them to rest for 5 to 10 minutes before serving. Serve warm with the chilled smoked paprika aioli for dipping.