Peel, wash and roughly grate the potatoes. Stir in egg. Season with salt and pepper. Heat 2 tablespoons of oil in a pan. Add 4 tablespoons of potatoes, form into 4 small Rösti and fry over low heat for about 5 minutes.
Turn the Rösti halfway through the frying time. Keep the finished Rösti warm. Fry the remaining 12 Rösti in the same way. Season sour cream to taste with salt, pepper and lemon juice. Divide the dip into small bowls and garnish with caviar.
Arrange hash browns, salmon and dip on plates. Garnish with dill.