Boil vinegar, sugar and water in a saucepan. Add the red onion and let the brine cool in the refrigerator.
Cut the carrots into very thin strips with a peeler. Heat oil in a saucepan. Test the temperature with a small piece of bread - bread should be golden. Roast the carrots in the hot oil for about 3 min. Remove them with a slotted spoon and let them drain. Lay the carrot fries on a paper towel and sprinkle with sea salt.
Stir the minced meat with salt and freshly ground black pepper. Form the meat into 4 burgers (about 10 cm in diameter). Melt the butter in a saute pan until golden. Fry the steaks about 1.5 min. on each side over a moderate heat for about 2 min. Cover the pan with a lid, remove it from the heat and let the steaks rest. Warm up the buns in the oven and cut them in half. Butter them with chili mayonnaise and add salad and sprouts on the bottom bun. Lay the cheese and the pickled red onions on the burgers. Add the top bun and serve with carrot fries.