Rinse the fresh spinach and dry the leaves thoroughly so the dish doesn't become watery. Cut the tomato into quarters, remove the seed cores, and dice the firm flesh into small pieces. Crack the three eggs into a bowl and add the sea salt and freshly ground black pepper. Beat everything together with a whisk for one minute, stirring vigorously until light and foamy.
Heat the olive oil in a skillet over medium-high heat. Place the spinach in the pan and cook, stirring frequently, for one to two minutes until the leaves just begin to wilt. Add the diced tomato and warm through for about half a minute. Then arrange the vegetables in an even layer over the bottom of the pan.
Lower the heat and pour the egg mixture over the vegetables. Allow the edges to set for approximately two minutes. Push the set edges inward with a spatula and tilt the pan so the still-liquid egg can run to the open spaces. Cook the omelet for another two to three minutes on low heat until the top is mostly set but the center is still slightly creamy.
Fold the omelet in half with the spatula in the pan. Slide the dish directly from the pan onto a plate and serve immediately.