Make the burger sauce. Add the mayonnaise, ketchup, mustard, pickle brine, diced pickles, sugar, and garlic powder to a small bowl. Season with a pinch each of salt and black pepper, and stir until thoroughly combined. Taste and adjust seasoning if needed.
Bake the fries. Preheat the oven according to the fry package directions. Arrange the frozen fries in a single layer on a large sheet pan and cook according to package instructions until golden and crispy. Season with salt immediately after removing from the oven.
Cook the onions. While the fries cook, melt the butter in a large skillet over medium-low heat. Add the onions and a small pinch of salt. Cook for 15–20 minutes, stirring frequently, until very soft and deeply golden. If the skillet becomes dry or browned bits begin sticking, add a small splash of water and scrape the bottom of the skillet. Transfer the onions to a bowl and tent loosely with foil.
Cook the beef. Return the same skillet to medium heat and add the olive oil. Add the ground beef and cook, breaking it into crumbles. Season with 1/2 teaspoon each salt and black pepper. Add the Worcestershire sauce and yellow mustard and stir to combine. Continue cooking until the beef is browned and completely cooked through.
Melt the cheese. Spread the cooked beef evenly across the skillet. Arrange the American cheese slices over the beef, cover with a lid and remove the skillet from the heat. Let stand for 2–3 minutes, or until the cheese has melted.
Assemble the bowls. Divide the finely shredded iceberg lettuce among four bowls. Top each with one-quarter of the cheesy burger meat, caramelized onions, and dill pickle slices. Add crispy fries and chopped Calabrian peppers, if using.
Finish and serve. Generously drizzle the burger sauce over each bowl and serve immediately while the beef and fries are hot and the lettuce is cold and crisp.