The Parisian Plunge

Start with the au jus. Melt the butter with the olive oil in a medium saucepan over medium heat. Add the sliced onion and a pinch of salt. Cook, stirring occasionally, for 10 to 12 minutes until the onions are soft, golden, and deeply caramelized. Do not rush this step.

Add the minced garlic to the caramelized onions and stir for 30 seconds until fragrant. Pour in the beef broth and water, then add the Worcestershire sauce, soy sauce, bay leaf, dried thyme, onion powder, and black pepper.

Bring the au jus to a boil, then reduce the heat to low and let it simmer gently for 10 minutes. The liquid should reduce slightly and the flavors should concentrate. Taste and adjust seasoning. Remove the bay leaf and keep the jus warm over the lowest heat.

While the jus simmers, preheat your oven's broiler to high with a rack positioned about 6 inches from the heating element.

Split the hoagie rolls lengthwise, leaving one edge intact as a hinge. Open them up and place them cut-side up on a sheet pan. Broil for 60 to 90 seconds until the cut surfaces are lightly toasted and golden. Watch carefully to prevent burning.

Remove the rolls from the oven. Lay 2 slices of provolone on the bottom half of each roll, overlapping them slightly.

Using tongs, briefly dip the sliced roast beef into the warm au jus, just 2 to 3 seconds per batch, enough to warm the meat and coat it in flavor. Pile the warmed beef generously onto the provolone-lined rolls.

Return the open-faced sandwiches to the broiler for 1 to 2 minutes, just until the provolone melts over the edges of the beef and begins to bubble. Remove immediately.

Close the sandwiches and press down gently. Slice each sandwich in half at an angle if desired.

Ladle the au jus through a fine-mesh strainer into small individual bowls or ramekins for dipping. Serve each sandwich alongside its own bowl of jus immediately while everything is hot.