Prepare dill cream: blend sour cream, shallots, lemon juice and dill. Season to taste with salt and pepper. Cover and refrigerate. This will be better made the day before for the flavors to fully develop, stir and taste again to adjust seasoning before serving.
Transfer the grated potatoes to a large mixing bowl and drizzle with melted butter. Season well with salt and pepper, sprinkle the flour evenly over the potatoes, and mix to fully coat the potatoes with the butter and flour. The little bit of flour will help the shredded potatoes stick together for easier flipping and ensuring that they stay whole for service.
Heat a small (6- to 7-inch) nonstick pan with 1 tablespoon oil over medium heat. Add 1/6 of the potatoes, press with spatula to flatten; cook until well-browned and crispy, about 2-3 minutes. Flip the potato cake over (or into another oiled heated pan); press cake flat with spatula and continue cooking until potato is crispy and browned and center is cooked through with no raw crunch.
Drain on paper towel or rack, then hold on a rack over a sheet pan in a 200° F oven.
Spread each galette with a generous amount of dill cream. Layer on 2 ounces of the sliced salmon, eggs and 1 teaspoon chives. Garnish with edible flowers, if desired. Serve immediately.
In a large bowl, beat the eggs with a fork until blended, then add the grated butter, mixing until well combined. The butter will emulsify into the eggs and keep them fluffy and tender, even when cooked through.
Heat a nonstick skillet over medium-low heat. Spray with nonstick spray. Pour the egg and butter mixture into the pan. Using a heat-proof rubber spatula, scramble the egg mixture gently until firm throughout, with no visible egg liquid remaining, and large curds have formed.
Season to taste with salt and pepper.
Note: Do not let uncooked egg mixture remain at room temperature for longer than one hour (including preparation and service time).