Combine beef broth, Worcestershire sauce, garlic powder, onion powder, dried thyme, and bay leaf in a medium saucepan. Bring to a simmer over medium heat and let it cook for 10 minutes while you prepare everything else.

Heat olive oil in a large skillet over medium heat. Add sliced onions with a pinch of salt and cook for 8 to 10 minutes, stirring occasionally, until golden and soft.

Slice hoagie rolls lengthwise, leaving one edge attached as a hinge. Spread softened butter on both cut sides of each roll.

Place buttered rolls cut side up on a baking sheet. Broil for 1 to 2 minutes until lightly golden, watching carefully to prevent burning.

Push caramelized onions to the side of your skillet. Add deli roast beef slices and gently warm them for 1 to 2 minutes per side.

Remove rolls from the oven and immediately place two slices of provolone on the bottom half of each roll. The residual heat will start melting the cheese.

Pile warm roast beef generously onto the cheese covered rolls. Top with caramelized onions and close the sandwiches.

Remove the bay leaf from your simmered au jus. Taste and adjust seasoning with salt and pepper as needed. Ladle the warm au jus into small bowls for serving alongside each sandwich.