In a blender, combine the jalapeños, vinegar, cilantro and garlic. Blend until smooth. Slowly add the vegetable oil while the blender is running until smooth. Add the mayonnaise and pulse to combine. Season with salt and pepper and whisk to combine.
Make the Slaw
In a large bowl, combine the green and purple cabbage, grated carrot and about 1 cup of the jalapeño vinaigrette. Toss to combine and add more vinaigrette if needed. Season with salt and pepper. Cover with plastic wrap and refrigerate until ready to serve.