Put the onion in a medium bowl and cover with 1/2 cup water. Set aside 30 minutes.
Meanwhile, puree the beef with 2 teaspoons water, the onion powder, 3/4 teaspoon salt and a few grinds of pepper in a food processor until smooth. Draw a 6-by-12-inch rectangle on a piece of parchment paper; flip over the paper so the pencil side is down (you should still be able to see the rectangle). Press the beef into the rectangle; cover with another piece of parchment and press until the beef is very thin and fills the rectangle completely. Uncover and score the beef into eight 3-inch-square patties. Poke 5 holes into each patty with a chopstick (one in the center and one near each corner). Slide the beef on the parchment onto a baking sheet, loosely cover with plastic wrap and freeze until firm, 10 to 15 minutes.
Trim the edges of the rectangle to make it even; cut patties along the scored lines. Heat an extra-large skillet over medium-high heat. Add the onion and liquid; bring to a boil. Stir in the butter and arrange the patties over the onion. Cook until the meat is no longer pink around the edges, 3 to 4 minutes. Put a bun bottom upside down on each patty. To steam the bun tops, rest each across 2 bun bottoms (like a bridge). Continue cooking until the patties are completely cooked through, about 2 more minutes, adding 1 to 2 tablespoons water if the skillet is too dry or if the onion starts browning.
Remove the bun tops from the skillet. Slide a spatula under each patty, picking up the onions and bun bottoms along with the meat; flip over onto a plate. Top each with a pickle and a bun top.