Heat 1/2 tablespoon of the olive oil in a medium-size skillet; add the onion, 1/8 teaspoon salt, and a pinch of pepper. Sauté over medium heat for 4 to 5 minute, until the onion is tender, then add the garlic and sauté for 1 minute. Transfer to a bowl and set aside.
Heat the remaining 1/2 tablespoon olive oil in the skillet and quickly wilt the spinach with 1/4 teaspoon salt over high heat. Transfer to a colander, drain, and cool. Using your hands, squeeze out the excess moisture and coarsely chop. Add the spinach to the onions along with the lemon zest and dill. Add salt and pepper to taste. The filling should be well seasoned.
Season the eggs with 1/4 teaspoon salt and a few pinches of pepper; add the water and whisk. Melt the butter in a seasoned omelet pan. When the butter is hot, add half the egg mixture. With a spatula, move the eggs toward the center of the pan as they begin to set on the edges. Tilt the pan so that the entire surface is covered again with wet eggs. As the eggs begin to set, place half the vegetable mixture in the center, then sprinkle with half the feta. Gently fold the omelet over and turn it out onto a plate. Repeat with the second omelet.
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