01 - Peel the russet potatoes and grate them using a box grater. Gather the shredded potatoes in a clean kitchen towel and squeeze firmly to remove as much excess moisture as possible. Transfer the dried grated potatoes to a mixing bowl.
02 - Add the melted butter, vegetable oil, garlic powder, onion powder, salt, and pepper to the grated potatoes. Toss thoroughly 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 patty roughly 4 inches in diameter. Place the patties on the hot skillet and cook for 3 to 4 minutes per side until deeply golden and crisp on both sides. Remove from the pan and keep warm.
04 - Gently shape the ground beef into 4 loose balls, being careful not to overwork the meat. Heat the skillet or griddle over high heat until smoking hot. Place the beef balls onto the cooking surface and immediately press down firmly with a heavy-duty spatula or burger press to flatten into thin patties. Season the top generously with salt and freshly ground black pepper.
05 - Cook the smashed patties for 2 to 3 minutes without moving them, allowing a deep brown crust to form and the edges to crisp. Flip each patty, lay one slice of sharp cheddar on top, and continue cooking for 1 to 2 additional minutes until the cheese is fully melted and the burger is cooked through.
06 - Spread a generous layer of burger sauce on the bottom half of each toasted bun. Layer on a lettuce leaf, a tomato slice, and a few rings of red onion. Place a crispy hash brown patty on top, followed by the cheesy smashed burger patty. Add dill pickle slices over the cheese and crown with the top bun.
07 - Serve the burgers hot while the hash browns are still crispy and the cheese is melted. Pair with crispy fries or a simple side salad if desired.