Melt 2 tablespoons butter in a large skillet over medium heat. Add sliced onions and cook for 12-15 minutes, stirring occasionally, until caramelized and golden brown. Season with salt and pepper, then transfer to a plate.
In the same skillet, combine beef broth, Worcestershire sauce, and garlic powder. Bring to a simmer.
Add the roast beef slices to the broth mixture and heat through for 2-3 minutes, stirring gently to coat all the meat.
Preheat your oven to 400°F. Split the hoagie rolls and butter the outsides with the remaining 1 tablespoon of butter.
Spread horseradish mayo on the inside of each roll. Using tongs, pile the roast beef onto the bottom halves, top with caramelized onions, and add 2 slices of provolone cheese to each sandwich.
Place sandwiches on a baking sheet and bake for 5-7 minutes until the cheese is melted and the bread is toasted. Serve with extra beef broth on the side for dipping!