To a large skillet, add olive oil and heat over MED HIGH heat. Add beef and cook, crumbling as it browns, for about 4-5 minutes. Drain beef and set aside on a plate.
To same skillet, add onion and cook another 4-5 minutes, stirring just occasionally, so the onions are softened, but a little charred on the edges. Add the beef back to the pan, along with the minced garlic. Cook about 1 minute.
Reduce heat to MED. Season with salt and pepper, then add in sauce ingredients (mayonnaise, vinegar, milk, dill, paprika, and pepper juice), and stir well to combine. Stir in peppers, Worcestershire sauce and ketchup.
Top with butter and stir until melted. In a small bowl, whisk together beef broth and cornstarch. Pour into the skillet and cook, stirring often, until thickened... usually about 5 minutes or so.
Serve on toasted buns with a slice of provolone cheese and a couple extra slices of pepperoncini peppers (optional)