For the chorizo-mushroom filling: Heat a large skillet over medium-high heat. Add the olive oil and chorizo, breaking up the sausage with a wooden spoon. Sprinkle with salt and pepper. Cook, stirring, until the sausage has slightly browned and is almost cooked through, about 3 minutes. Add the mushrooms. Cook, stirring occasionally, until the mushrooms begin to brown and the sausage is fully cooked, about 5 minutes more. Transfer to a bowl and stir in the salsa. Taste for seasoning and set aside.
For the beef and potato filling: Heat the olive oil in a medium skillet. Add the ground beef and cook until browned, breaking it up with a wooden spoon. Add French fries and cook until warmed through. Season with salt and pepper. Transfer the filling to a bowl and set aside.
For the beef and olive filling: Heat the olive oil in a medium skillet over medium-high heat. Add the garlic and cook until beginning to brown. Add the ground beef and cook for 1 minute. Add the red pepper and a pinch of fiesta seasoning. Add the olives and another pinch of fiesta seasoning. Cook until the beef is cooked through and browned, and the veggies are softened, 5 to 8 minutes. Remove the filling to a bowl and set aside.
Make the empanadas: Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
Lay out the empanada wrappers on a flat surface. Place 1 heaping tablespoon of filling in the center of each wrapper; brush the wrapper edges with water, then fold over to form a half-moon pocket. Use a fork to crimp and seal the edges.
Place the empanadas on the parchment-lined baking sheet and bake until golden brown, 20 to 30 minutes. Let cool slightly before serving.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.