In a large bowl, whisk together the honey and vinegar. Drizzle in the olive oil while whisking. Season with salt and pepper.
Remove tough outer leaves and core from the cabbages. Thinly slice.
Toss the cabbage, shredded carrot, cucumber, and lemon zest with the dressing. Toss to coat.
Serve immediately as a salad, or store in the fridge overnight for a slaw that’s more pickled.