In a blender or using an emersion blender, combine the minced garlic, 1 cup of cilantro, lime juice, vinegar, salt, pepper, mayonnaise, and honey.
On medium speed, blend these ingredients until well incorporated.
With the blender on low, begin to drizzle in the olive oil.
In a large mixing bowl, combine the shredded brussels sprouts and broccoli slaw. Pour dressing over and toss to combine well. Let the mixture sit for 30 min, up to six hours, before serving.