Pour about ⅓ cup of dressing into a bowl. Add the chicken, stir to coat, then refrigerate.
Prepare the edamame according to the package directions. Drain, then transfer to a paper towel–lined plate to dry.
In a large bowl, combine the cabbage, carrot, scallions, almonds, parsley, and edamame. Add the sugar, vinegar, and salt and mix well. Cover and refrigerate for 30 minutes, stirring once or twice.
Just before serving, add the chicken and noodles and toss well to combine. Mix in only as many noodles as will be eaten at each service. Noodles that sit in the salad will get soggy. Pass the remaining dressing at the table.
Put all of the ingredients into a blender and pulse to a purée that is smooth and full-bodied, not thin. Taste and adjust the seasonings, if desired. Transfer to a container. Cover and refrigerate. Bring to room temperature and shake before using.
Makes about 1 ¼ cups.