In a medium bowl, whisk the eggs and water, just until blended. Add salt and pepper to taste.
Place the skillet, wiped clean, over medium heat 2 minutes. Add the butter, swirling it to coat the pan. When the butter stops sizzling, pour the egg mixture into the pan. Reduce the heat to low and cook until the bottom is set, about 10 seconds. Using a rubber spatula or a wooden spoon, pull the set eggs at the edges of the pan toward the center, allowing the unset eggs to run from the center to the sides. (Adjust the heat if necessary to prevent browning.) Continue to cook until a thin layer of unset egg is visible on top. The total cooking time should be less than 2 minutes.
Remove the pan from the heat; spoon the spinach mixture across the middle third of the omelet; sprinkle with the feta and dill. Using a spatula, fold the third of the omelet nearest the handle over the center third with the filling. Holding the handle, tilt the pan so that the omelet rolls out of it and onto a plate, seam side down.