Special equipment: a 4-inch round cookie cutter
Position 2 racks in the middle of the oven and preheat the oven to 425 degrees F. Line 2 large baking sheets with parchment.
Stir together the ketchup, mayonnaise, chopped pickles and mustard in a medium bowl. Season with salt and set the sauce aside.
Heat the oil in a large skillet over medium-high heat. When it starts to shimmer, add the ground beef, a pinch of salt and a few grinds of pepper. Cook, breaking the meat apart with a wooden spoon or heatproof spatula, until lightly browned in spots and just cooked through, 3 to 4 minutes. Add the onion and cook, stirring constantly, until crisp-tender, about 2 minutes. Use a large slotted spoon to scoop the meat mixture into a medium bowl and stir in 1/3 cup of the sauce. Allow to cool slightly. Fold the American cheese into the cooled mixture.
Lightly beat the egg with 1 tablespoon of water in a small bowl for the egg wash and set aside.
Unfold 1 puff pastry sheet onto a lightly floured surface. Roll out into a 12-inch square. Cut out 9 rounds with a 4-inch round cookie cutter. Spoon 1 leveled tablespoon of the meat filling just off center on each round. Top the filling with 1 whole pickle chip. Brush the edge of each round with the egg wash and fold the puff pastry over the filling, slightly stretching if necessary. Press the edges together and crimp the edges with a fork. Transfer to one of the prepared baking sheets and brush each empanada with more egg wash. Repeat this process with the remaining sheet of puff pastry and filling. Bake until puffed and golden brown, about 15 minutes. Serve hot with the remaining sauce for dipping.
Copyright 2017 Television Food Network, G.P. All rights reserved.