Combine the mayonnaise, horseradish and lemon juice. Add salt and pepper to taste. Store in the refrigerator until ready to use.
In a saucepan add the olive oil and heat to medium. Add the carrots, celery and leaks and sauté until softened. Add the stock, peppercorns, red pepper flakes and bring to a simmer. simmer for about 15 minutes. Strain the broth, discarding the solids and keep warm for serving.
Preheat the broiler. Thinly slice your beef tenderloin and set aside. Split your french bread or hoagie rolls if not already split. Place on a sheet pan, outside up and toast for just about a minute or less. Remove and slather with butter. Return to the sheet pan and under the broiler until the roll is toasted and starting to brown a little on the edges. Remove, add the cheese and return and just melt.
Remove from the oven, slather the horseradish mayonnaise on each side, pile high with the beef, red peppers and the greens. Serve with individual bowls of the au jus.