Delicious fried cheese-stuffed wonton chips with nacho toppings.
Make the beef: Heat the vegetable oil in a large skillet over medium heat. Add the onion and cook until translucent, about 5 minutes. Add the garlic and cook for 1-2 minutes more, until softened but not browned.
Add the beef, cumin, chili powder, oregano, salt, and pepper to the pan. Stir to break up the ground beef, then let sit undisturbed for about 3 minutes to let the meat brown. Stir and continue cooking until no pink remains, 5-7 minutes total. Add 2 tablespoons of the pickled jalapeño liquid and cook until slightly evaporated, about 1 minute. Remove the pan from the heat. Drain any excess liquid from beef and set aside.
Make the wontons: In a medium bowl, mix together the American cheese and beef until well combined with large chunks of cheese still intact.
Fill a large, deep pot about ⅔ of the way with vegetable oil. Heat the oil until it reaches 350°F. Set a wire rack on top of a baking sheet.
On a clean work surface, lay out 10 wonton wrappers at a time. Scoop about 2 teaspoons of the beef mixture into the center of each wonton wrapper. Lightly brush 2 edges of the wrapper with egg, then fold up one corner to meet the opposite corner, forming a triangle, and gently press all the edges together to seal, ensuring all the air is pressed out from around the filling. Repeat with the remaining filling and wrappers.
Working in batches, gently lower 4-6 filled wontons into the hot oil. Fry until golden brown, flipping once, 2-3 minutes total. Transfer to the wire rack to drain and sprinkle lightly with salt.
Arrange half of the stuffed wontons on a baking sheet. Cover with ½ cup of the shredded cheddar and about half the black beans. Top with the remaining wontons and cheddar cheese.
Broil the wontons until the cheese is melted and bubbly, about 2 minutes.
Top the wonton nachos with the remaining black beans, jalapeños, red onion, tomato, sour cream, avocado, and cilantro. Serve with lime wedges on the side.