Prepare the Hash Browns: Place the grated potatoes in a clean kitchen towel and squeeze out as much moisture as possible. In a bowl, combine the grated potatoes, flour, garlic powder, onion powder, salt, and pepper. Mix until evenly coated.

Cook the Hash Browns: Heat 1 tablespoon of olive oil or butter in a non-stick skillet over medium heat. Add the potato mixture to the skillet, pressing it down to form a flat layer. Cook for about 5-7 minutes, or until golden brown and crispy on the bottom. Flip the hash browns and cook for an additional 5-7 minutes until crispy and golden on the other side. Remove from the skillet and keep warm.

Make the Herb Cream Cheese Filling: In a small bowl, mix the softened cream cheese, smoked salmon, dill, and chives until well combined. Set aside.

Prepare the Omelet: In a bowl, whisk together the eggs, milk, salt, and pepper until frothy. Heat a non-stick skillet over medium-low heat and add a small amount of butter or oil. Pour the egg mixture into the skillet, swirling to coat the bottom evenly. Allow to cook undisturbed until the edges begin to set, about 2-3 minutes.

Fill the Omelet: Once the omelet is set but still slightly runny on top, spoon the herb cream cheese mixture onto one half of the omelet. Carefully fold the other half over the filling and let cook for an additional 1-2 minutes until fully set.

Serve: Slide the omelet onto a plate alongside the crispy hash browns. Garnish with additional fresh chives before serving.