In a food processor or blender, combine the shallots, ginger, chiles, garlic, and galangal, and puree to a smooth paste.
Bring the Coconut Milk to a boil in a wok, add the paste, reduce the heat slightly, and cook, stirring occasionally, for about 5 minutes. Add the tomato and the eggplant and cook for 5 more minutes.
Add the catfish, beans, cilantro leaves, and fish sauce, and cook over medium heat for 10 minutes or until the beans are tender. The curry should be quite liquid, so add some water or fish stock if necessary.