Securely hold the green cabbage, and carefully cut down through the stem to create two halves. Place the cut side down on the cutting board. Cut each cabbage half into quarters by cutting down through the stem. Flip the quarters over and carefully remove the thick core with a knife. There should be four wedges. Repeat the process with the purple cabbage.
Use a chef's knife to cut the green and green cabbage into ¼-inch thick slices, or use a mandoline to shred the cabbage.
Peel and shred the carrots using a grater, peeler, or cut them into ⅛-inch thick slices. For convenience, pre-shredded carrots can be used.
In a large bowl combine the green cabbage, red cabbage, and carrots.
In a medium-sized bowl whisk together mayonnaise, sour cream, honey, apple cider vinegar, lemon juice, salt, pepper, and celery seeds if using.
Right before serving, drizzle half of the coleslaw dressing and toss to combine. Add more dressing as desired or serve the rest on the side.
Quicker Version: Use pre-shredded cabbage and carrots, and store-bought mayonnaise.
Yield: The dressing makes ¾ to 1 cup.
Make-Ahead: The dressing can be made ahead of time and stored for up to 3 days in an airtight container. Add right before serving for the best vegetable texture.