Position an oven rack 6-inches from the broiler, and preheat the broiler to high heat.
Toss the cucumber, vinegar, and 1 tablespoon of the olive oil together. Season with salt and pepper and set aside.
Warm a medium nonstick skillet over medium-low heat. Whisk the egg whites in a large bowl until foamy and doubled in volume; season with salt and pepper and whisk in the dill. Add the remaining 1 tablespoon olive oil to the skillet. Pour the whites into the skillet and swirl to cover entire skillet. Cook, without stirring, until the whites are almost set and light brown on the bottom, about 3 minutes.
Place the skillet under the broiler and cook until the omelet sets and begins to brown, about 30 seconds. Spoon half of the cucumber salad onto half of the omelet and fold the omelet over the filling. Transfer omelet to a serving platter and scatter the remaining cucumber salad on top. Serve with the smoked salmon on the side.
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