Shred the green cabbage and red cabbage into thin 1/8-inch strips using a mandoline or sharp knife for uniform texture. Slice the radishes into thin matchsticks—this creates better crunch than dicing and helps them stay crisp longer. Grate the carrot using a box grater or microplane. Finely dice the green onion and chop the cilantro. I find that cutting everything to similar sizes helps the slaw feel cohesive and ensures even dressing distribution.

In a small jar or bowl, whisk together the extra virgin olive oil, apple cider vinegar, honey, freshly grated ginger, lime juice, salt, and black pepper. Stir vigorously or shake in the jar until the honey dissolves completely and the dressing emulsifies slightly. Taste and adjust seasoning if needed—I like to add an extra pinch of salt here since it brings out the sweetness of the vegetables.

Transfer all the prepared vegetables from Step 1 to a large bowl. Pour the dressing from Step 2 over the vegetables and toss thoroughly with tongs or your hands until everything is evenly coated. Let the slaw sit for 5-10 minutes to allow the vegetables to soften slightly and the flavors to meld. Top with toasted sesame seeds just before serving to keep them crunchy and preserve their nutty flavor.