Rinse the tomato and cut it into small cubes. Remove the skin from the half avocado and slice the flesh into thin slices. Pluck the leaves from the fresh basil. Break the three eggs into a bowl. Add salt and pepper and beat well with a fork or whisk until an even mixture.
Heat the tablespoon of olive oil in a frying pan over medium-high heat. Pour the egg mixture into the pan and let the bottom set briefly. Then immediately distribute the tomato cubes evenly over the still-liquid top. Let the omelet cook gently for a few minutes until the edges begin to release from the pan and the top is almost completely dry and set.
Carefully slide the cooked omelet from the pan onto a plate. Distribute the sliced avocado over the warm eggs. Sprinkle the fresh basil leaves over the omelet and avocado. Serve immediately.