In a food processor, combine all the ingredients for the remoulade. Pulse a few times to combine. Cover the remoulade and pop it in the fridge while you make the burgers.
Put the beef in a large mixing bowl. Use a rubber spatula to fold in the horseradish and chives; season with salt and pepper. Hand-form the meat into 8 burgers, cover them, and set them aside in the fridge while you prepare your grill.
Preheat a gas or charcoal grill and get it very hot. Burgers stick to a cold grill, so itâ€™s important that you give the grill plenty of time to heat. Here is a restaurant tip to keep food from sticking to your grill: Take a few paper towels and fold them several times to make a thick square. Blot a small amount of oil on the paper towel; then carefully and quickly wipe the hot grates of the grill. This will create a nonstick grilling surface. Grill the burgers for 8 minutes per side for medium; 7 minutes if you like your meat rare. If you like well done, I canâ€™t help you.
When the burgers are just about cooked, put a couple of slices of cheese on top of each and cover the grill for 1 minute to melt the cheese. Remove the burgers to a clean side plate so you have enough room to toast the buns.
Rub the grill rack with the same paper towel as before to clean off the small charred pieces; then toast the hamburger buns cut side down for 1 minute. Serve the burgers with the tomato remoulade and any garnish you like, such as bacon, lettuce, sliced tomato, or onion.
Edited: October 12th, 2009