In a bowl, combine the mayonnaise, vinegar, capers, mustard, horseradish, pickle and green onion. Season with salt and pepper. Add the celeriac and mix well. Let marinate while you prepare the burgers.
In a food processor, finely chop the bacon and bread. Transfer to a large bowl.
Add the meat and cheese to the bowl. Lightly season with salt and pepper. Mix well. With your hands, form the mixture into 6 patties. Place on an oiled plate. Lightly oil the patties and refrigerate for 15 minutes.
Preheat the grill, setting the burners to high. Oil the grate.
Grill the patties for 6 minutes on each side or until cooked through. Toast the hamburger buns.
Place a patty on each bun bottom and top with the remoulade. Close with the bun tops and serve.