Mix all of the burger sauce ingredients together, and chill until needed.
Divide the beef into 14 equal mounds. Sprinkle the top of each mound with salt and pepper.
Gently heat a flat griddle pan. Once warm, brush the inside of the burger buns with butter and cook, butter side down, for 1 minute or so until golden brown. Put the buns to one side, wipe the pan clean, and turn up the heat.
When the pan is smoking hot, place two of the beef mounds - seasoning side down - onto the hot pan. Using the wide spatula, flatten each patty by pressing down firmly. The patty should be less than 1 centimetre thick and as big as the burger buns. Don’t move the patties as they cook, but keep pressing down with the spatula to create maximum crust. Once the tops of the burgers start to look cooked, carefully scrape them up from underneath, so that the crust stays intact, and flip them over. Top with a slice of cheese and cook for another 30 seconds, then remove from the pan.
Put burger sauce on the bottom half of each bun. Place the burger patties straight from the pan in a stack onto the dressed bun, topped with pickled gherkin slices and the brioche bun lid.
Eat immediately, with French fries and extra pickles.