In a medium sized bowl, whisk egg then whisk in milk and flour until mixture becomes thick. Stir in potatoes. Liberally salt and pepper.
Heat a skillet over medium heat. Melt 1 teaspoon clarified butter. Ladle 1/4 cup boxty batter. Cook 4 minutes, or until exterior becomes crispy. Flip and cook an additional 4 minutes. Remove from heat. Melt more butter on pan and repeat process with remaining boxty batter.
To serve: garnish each boxty pancake with 2 slices of salmon, 1 teaspoon crème fraîche, and a generous pinch of dill.