Place the grated potatoes in a clean kitchen towel and squeeze out as much moisture as possible. Transfer the dried potatoes to a large bowl.
Add salt, black pepper, flour, and the beaten egg to the bowl with the potatoes. Mix until well combined.
Heat the vegetable oil in a large skillet over medium heat.
For each rosti, scoop about 1/4 cup of the potato mixture into the skillet, flattening it with a spatula to form a patty. Cook for about 4-5 minutes on each side, or until golden brown and crispy. Repeat with the remaining mixture, adding more oil as needed.
Once cooked, transfer the rostis to a paper towel-lined plate to drain excess oil.
In a small bowl, mix together the sour cream, dill, lemon juice, and garlic powder.
To assemble, layer a rosti on a plate, top with a slice of smoked salmon, and add a dollop of the sour cream mixture. Repeat the layers, finishing with a rosti on top.
Serve immediately and enjoy!