Wash and dry the spinach then chop it coarsely.
Heat the butter in a large nonstick ovenproof skillet over medium heat. Stir in the sun-dried tomato and scallion and cook, stirring, until the scallion is wilted, about 2 minutes. Season lightly with salt and pepper. Stir in the spinach and cook until wilted and the water it gives off is evaporated, about 4 minutes.
Meanwhile, in a mixing bowl, beat the eggs with salt and pepper to taste.
Lower the heat to medium. Pour in the eggs and let them sit a few seconds until they start to set around the edges. Using a plastic spatula push a piece of the set edge gently toward the center. Tilt the pan and let some of the unset egg from the top fill the little gap you just made. Keep going around the edge of the pan like this, until there is no more unset egg on top.
Scatter the goat cheese slices over the top of the omelet. Put the skillet under the broiler and leave the oven door open, cook just until the top of the omelet is set and puffed, about 2 minutes.