Grate the potatoes and squeeze out any excess moisture. In a bowl, combine the potatoes, egg, flour, salt, and pepper.
Heat olive oil in a skillet over medium heat. Drop spoonfuls of the potato mixture into the hot oil to form the rosti patties. Cook for 2-3 minutes per side, until golden brown and crispy. Drain on paper towels.
Season the beef patties with salt and pepper on both sides. Cook in a skillet or on a grill for 3-4 minutes per side, or until cooked through.
Toast the hamburger buns in a skillet or on a grill until the cut sides are golden brown and crispy.
Wash the lettuce leaves, and slice the tomatoes and red onion into thin rings.
Assemble the burgers: place lettuce leaves on the bottom bun, followed by the beef patty, rosti, tomato slices, and red onion rings.
Top with the remaining bun and gently press down. Serve immediately with a fresh salad or french fries.
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