Separate the egg yolks and whites into 2 separate medium bowls. Add 1 tablespoon of water to the egg whites and, using a hand mixer, beat on medium-high speed until medium peaks form, 4 to 5 minutes.
Season the yolks with salt and pepper and beat until smooth, thickened and slightly pale in color. Fold one-third of the egg whites into the egg yolks and thoroughly mix until there are no streaks. Add half of the Gruyere and the soda water. Pour in the remaining egg whites and gently fold to combine.
Melt the butter in a 10-inch nonstick skillet over medium heat until it foams, then pour in the egg mixture, smoothing the top. Cover the skillet and cook until the omelet is golden brown on the bottom and you can lift the edges to peak underneath, about 5 minutes.
Sprinkle the remaining cheese and the herbs on top, cover the skillet and cook 2 more minutes. Remove the pan from the heat and keep covered until the cheese melts, about 1 minute. Fold over and serve.