Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-low heat. Add the thinly sliced onions and cook slowly, stirring occasionally, for 15-20 minutes until deeply caramelized and tender. This step is crucial for flavor.

Increase heat to medium-high. Add the minced garlic to the pot with the onions and cook for 1 minute until fragrant.

Add the very thinly sliced ribeye steak to the pot. Season with salt and freshly ground black pepper. Cook, breaking up the meat with a spoon, until the steak is browned and cooked through, about 3-5 minutes. Remove any excess grease if desired.

Sprinkle the all-purpose flour over the steak and onion mixture. Stir well to coat everything and cook for 1 minute, allowing the flour to cook out its raw taste.

Gradually whisk in the beef broth, ensuring no lumps form. Bring the soup to a gentle simmer, scraping any browned bits from the bottom of the pot. Stir in the Worcestershire sauce and dried thyme.

Reduce the heat to low, cover, and let the soup simmer for 15-20 minutes, allowing the flavors to meld and the soup to thicken slightly.

Stir in the heavy cream and cook for another 5 minutes, ensuring the soup does not boil after adding the cream.

While the soup simmers, prepare the croutons. In a small bowl, toss the 1-inch hoagie roll cubes with melted butter. You can toast them in a dry skillet over medium heat for 5-7 minutes until golden and crispy, or spread them on a baking sheet and bake at 375°F (190°C) for 8-10 minutes.

Ladle the hot soup into individual bowls. Top each serving with 1-2 slices of provolone cheese, allowing it to melt slightly from the heat of the soup. Garnish with the toasted hoagie croutons and fresh chopped parsley, if desired. Serve immediately.