Make the sauce. Combine the Greek yoghurt, smoked paprika, garlic powder, ketchup, creamed horseradish and Worcestershire sauce in a bowl. Mix until smooth and season with salt and ground white pepper. If the yoghurt is watery, strain it first. Refrigerate for 30 minutes so the flavours develop.
Prepare the patties. Divide the beef mince into 8 loose 75g (2.6oz) portions and roll into balls, without overworking the mince. Combine the smoked paprika, onion powder, salt and black pepper in a small bowl.
Heat the pan. Place a cast iron or heavy-based frying pan over high heat for 3 minutes, then lightly coat with the neutral oil.
Smash the patties. Working in batches of 2-3, place the beef balls in the hot pan. Cover each with baking paper and firmly smash into patties about 1cm (⅜ inch) thick. Immediately season the exposed side with the spice mix.
Cook and flip. Cook for about 90 seconds, until the edges are deeply browned and crispy. Scrape firmly underneath each patty to keep the crust, then flip.
Add the cheese. Place a cheese slice on each patty and cook for another 20-30 seconds, until the beef is cooked through to 71°C (160°F) and the cheese has melted. Stack two patties to make each double burger. Repeat with the remaining patties.
Toast and assemble (to serve fresh). Toast the cut sides of the buns in the pan for about 1 minute. Spread the sauce over the bottom and top of each bun, then add the double smash patties.
Meal prep. Let the patties cool for about 15 minutes. Portion each double burger into a meal prep container and keep the sauce separate in a small airtight container.