Combine mayo, horseradish, and lemon juice into a bowl and combine.
In a medium size pan over medium heat add olive oil. Sauté carrots, celery, and leeks for 6 - 8 minutes or until soft. Add beef stock, peppercorns, chili pepper flakes, and salt and bring to a simmer for additional 15 - 20 minutes.
Strain solids and reserve warm liquid for the Au Jus. Discard the solids.
French Dip Sandwich
Turn on broiler on high. Slice the rolls open and add the provolone. Place under broiler on middle rack and remove when cheese melts, about 3 minutes.
Place remaining ingredients on the sandwich and then close the roll. Don't cut sandwich up, as it will make it easier to dip into the Au Jus.
We love to use leftover Prime Rib for these sandwiches.