Prepare the Big Mac Sauce. In a medium bowl, whisk together mayonnaise, relish, mustard, paprika, sugar, onion powder, Worcestershire sauce, garlic powder, salt, and pepper. Refrigerate until ready to use.
Rehydrate the onions. Mix the minced dried onion with the water and set aside.
Form the patties. Divide the ground beef into 8 portions and shape into thin patties. Season with salt and pepper.
Cook the patties. In a large skillet over medium-high heat, cook 4 patties at a time, flipping once, until cooked through (about 2 minutes per side). Set aside on a paper towel-lined tray and repeat with the remaining patties.
Drain the onions. Scoop the rehydrated onions out of the water and place them on a paper towel-lined plate.
Toast the buns. Melt butter in a large skillet over medium-high heat. Lightly toast all the buns and set aside.
Assemble the burgers. Start with the bottom bun and spread on Big Mac sauce. Add cheese, lettuce, pickles, a patty, and onions. Top with another bottom bun, more sauce, lettuce, pickles, a patty, onions, and finally the top bun. Repeat with remaining burgers and serve!