Cut off the bottom portion of the stalks of the watercress and discard. Rinse the watercress leaves and tender stalks. Press between two kitchen towels to remove the water. Or use a salad spinner.
Heat the cooking oil in a frying pan. Saute the garlic and ginger until aromatic. Add the chopped tomato. Sprinkle with salt and pepper. Cook, stirring often, until the tomato pieces are very, very soft.
Add the watercress. Sprinkle with more salt and pepper. Cook over medium heat, uncovered and with occasional stirring, until the greens are tender. By the time the dish is done, there should be very little liquid left.
Serve as a side dish or a vegetarian main dish.