Toss grated potatoes in 1/4 pound clarified butter. Season with salt and freshly ground pepper.
Heat 2 non-stick saute pans over high heat until nearly smoking. Divide remaining butter between the 2 pans. Add the potatoes evenly to each pan, and shape them into thick pancakes. Cook for 1 to 2 minutes, then reduce heat. Saute until almost golden brown. Use a spatula to check the underside of the pancake, turn over and cook other side until golden. Remove galettes from pans and warm in a preheated 425 degree F. oven for 10 minutes.
Prepare dill cream: In a bowl, mix together shallots, dill, creme fraiche or sour cream, juice of 1/2 lemon and season with salt and pepper. Mix well.
Remove galettes from oven while still warm. Spread with dill cream and cover with slices of smoked salmon. Lightly brush smoked salmon with olive oil, then sprinkle with black pepper and remaining lemon juice. Cut galettes into desired portions and garnish with caviar and chopped chives. Serve immediately.