Step 1

Heat oven broiler to high.

Step 2

Using drippings from roast beef pan, spoon out most of oil, if applicable. Place roasting pan over medium high heat on stove top. Add beef stock and soy sauce to pan and, using a wooden (or non-abrasive) spoon, scrape off browned bits from the pan. Bring to a simmer and cook until reduced by half, about 8-10 minutes. If sauce is too salty, add more beef broth. If not salty enough, add more soy sauce, as needed, until it reaches desired flavor.

Step 3

Slice hoagie rolls in half, lengthwise. Spread a thin layer of butter over each half (top and bottom) of roll. Place rolls, butter side up, on a baking sheet lined with aluminum foil. Place bread under the broiler and broil until butter is melted and bread starts to turn golden brown. Careful not to let bread burn. Once golden brown, remove from oven. Take the "tops" off the baking sheet and set aside. Leave the "bottoms" on the baking sheet for later. Keep broiler on.

Step 4

Slice roast beef into very, very thin slices. Place slices in hot Au Jus on the stove and cook for 1 minute. Using tongs or a fork, carefully remove roast beef slices and layer on each "bottom" half of the sandwich with desired amount. Top each with a slice of provolone cheese and replace under the broiler until cheese is melted, about 1-2 minutes.

Step 5

Remove from broiler and place the "top" half on each sandwich. Slice each french dip in half and serve alongside a small cup of Au Jus (and a dab of horseradish, if desired) for dipping.