In a large mixing bowl, add the beef mince, horseradish, Dijon mustard, crushed garlic, pepper and salt. Mix using your hands until well combined.
Divide the beef mixture into 16 equal portions (approx 65-70g each). Shape each portion into a small burger patty and set aside. If making in advance, cover and place into the refrigerator until required.
Prepare the burger sauce by combining the mayonnaise, tomato ketchup, pickled cucumbers, Dijon mustard, lemon juice and sriracha in a small bowl. Stir with a spoon until well combined and refrigerate until serving.
Prepare the burger toppings by slicing the brioche buns and cheese slices in half. Place the brioche buns into the toaster so that they are ready for toasting (don't toast them just yet).
Heat a dash of olive oil in a large non-stick frying pan over medium-high heat. Add the burger patties and cook for 3-5 minutes per side, or to your liking. Just before the end of the cooking time toast the brioche buns for about 1 minute.
Assemble the sliders by placing 1-2 tsp of burger sauce on the bottom half of the bun. Top with a burger patty, cheese slice, a couple of slices of pickled cucumber and 1 tsp of tomato ketchup. Finish with the top half of the bun and skewer with a bamboo pick to hold everything in place. Serve immediately with a side of chips, pickles, and any leftover special sauce.