1. Cut broccoli florets from stems; separate florets into small pieces using a paring knife. Peel away tough outer layer of stems; finely chop stems.
2. Whisk together mayonnaise and next 6 ingredients in a large bowl; add cabbage, raisins, and broccoli, and stir to coat. Cover and chill 1 hour. Stir in pecans just before serving.
*1 (16-oz.) package coleslaw mix may be substituted.