Put all but 2 tablespoons of the scallions in a blender; add the ginger, jalapeno, brown sugar, fish sauce, soy sauce, vinegar, tomato and 1/4 teaspoon salt and blend until smooth. Transfer to a 6-quart slow cooker.
Add the chicken and mushrooms to the slow cooker and stir to coat. Cover and cook on low, 4 hours.
Roughly chop the watercress and stir into the slow cooker. Serve the chicken and vegetables with rice; top with the reserved scallions.