Toss grated potatoes in 1/4 pound clarified butter. Season with salt and freshly ground pepper.
Heat 2 non-stick sauté pans over high heat until nearly smoking. Divide remaining butter between two pans. Add the potatoes evenly to each pan, and shape them into thick pancakes. Cook for 1 to 2 minutes, then reduce heat. Sauté 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 425°. oven for 10 minutes.
In a bowl, mix together shallots, dill, crème fraîche 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 and sturgeon. Lightly brush the salmon and sturgeon 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.