Preheat oven to 375°F. Line a baking sheet with parchment paper (optional)
Heat olive oil or butter in a skillet over medium-low heat. Add the onion with a small pinch of salt and cook for 10–15 minutes, stirring occasionally, until softened and golden brown. Transfer to a bowl.
Add ground beef to the skillet. Cook, breaking the beef into small crumbles, until browned and cooked through. Drain excess grease if needed.
Add Worcestershire sauce, garlic powder, paprika, salt, and black pepper. Stir and cook for approximately 1 minute.
Remove from heat and stir in the finely chopped dill pickles. Allow the mixture to cool slightly.
Flatten each biscuit into a small circle. Add approximately 1½ tablespoons beef mixture to the center. Top with caramelized onions and ½ slice American cheese.
Pull the edges of the biscuit around the filling and pinch tightly to seal. Place seam-side down on the prepared baking sheet.
If using, whisk the egg with a splash of water and lightly brush over the tops of the bombs. Sprinkle with sesame seeds.
Bake for 13–15 minutes, until the biscuits are puffed and golden brown.
Let cool for several minutes before serving.
For the special sauce, stir all sauce ingredients together until smooth. Serve alongside the warm cheeseburger bombs.