01 - Peel the russet potatoes and grate them using a box grater. Gather the shredded potatoes in a clean kitchen towel and wring out as much moisture as possible. Transfer the dried potatoes to a mixing bowl.
02 - Add the melted butter, vegetable oil, garlic powder, onion powder, salt, and pepper to the grated potatoes. Toss everything together until the seasonings are evenly distributed throughout the mixture.
03 - Heat a large nonstick skillet or flat griddle over medium-high heat. Divide the seasoned potato mixture into 4 equal portions. Press each portion into a thin round patty about 4 inches across. Place the patties on the hot surface and cook for 3 to 4 minutes per side until deeply golden and crisp. Transfer to a plate and keep warm.
04 - Gently shape the ground beef into 4 loose balls, handling the meat as little as possible. Wipe the skillet or griddle clean and return it to high heat. Once the surface is smoking hot, set the beef balls on it and immediately press each one flat with a heavy-duty spatula or burger press. Season the flattened patties generously with salt and pepper.
05 - Let the patties cook undisturbed for 2 to 3 minutes until the bottoms develop a dark crust and the edges turn crispy. Flip each patty, lay a slice of cheddar on top, and continue cooking for 1 to 2 more minutes until the cheese is fully melted.
06 - Spread a generous layer of burger sauce on the bottom half of each toasted bun. Stack a lettuce leaf, a tomato slice, and a few rings of red onion on top. Add a crispy hash brown patty, then place the cheesy smash burger over it. Finish with pickle slices and cap with the top bun.
07 - Serve the burgers hot while the hash browns are still crisp and the cheese is gooey. Pair with crispy fries or a simple side salad if desired.