Trim the leeks and wash carefully. Drain them and slice into thin rounds.
Heat the olive oil in a large nonstick saucepan. Add the grated ginger, turn with a spoon, then add the cumin powder. Add the sliced leeks, season and cook for around 10 minutes, stirring regularly. If necessary, add 1 or 2 tablespoons of water to keep the mixture from sticking. Season to taste.
Add the cooked rice to the pan and fluff up the grains with a fork. Serve hot.