Place the greens in a colander; drain well. Heat the oil in a large saucepan over medium heat. Add the garlic, jalapenos and onion. Cook, stirring, 2 minutes. Stir in the ginger, broth, salt and pepper. Cover, simmer 15 minutes.
Increase the heat to high. Stir in the greens. Cook until greens are immersed in the liquid, 2 minutes. Cover saucepan. Reduce the heat to medium low. Cook, stirring occasionally, until tender, about 20 minutes.