Remove outer leaves from the green and red cabbage. Quarter each cabbage, core them, then thinly slice across the grain to yield fine shreds. Measure out 4 cups shredded green cabbage and 2 cups shredded red cabbage and place in a large mixing bowl.

Prepare vegetables

Peel and shred the carrots (or use a box grater) to make about 1 cup packed. Trim radishes and slice them very thin (mandoline or knife) to yield 1 cup. Peel and halve the yellow onion; slice very thin and lightly separate into 1/2 cup. Seed the jalapeño (for less heat) and mince finely, about 1 small jalapeño.

Add the shredded carrots, sliced radishes, thin onion, and minced jalapeño to the bowl with the cabbages. Toss gently to combine and ensure an even distribution of ingredients.

Dressing

Whisk dressing

In a separate medium bowl, combine 1/2 cup mayonnaise, 2 tablespoons apple cider vinegar, 1 tablespoon lime juice, 1 teaspoon Dijon mustard, 1 teaspoon honey, 1 teaspoon salt, 1/2 teaspoon black pepper, and 1/4 teaspoon ground cumin (optional). Whisk vigorously until smooth and slightly emulsified. Taste and adjust seasoning: add more vinegar or lime for tang, more honey for sweetness, or more salt as needed.

Combine & Finish

Pour the dressing over the bowl of prepared vegetables. Using two large spoons or salad tongs, toss thoroughly until all strands and slices are evenly coated. If the slaw feels dry, add an extra tablespoon of mayonnaise or a splash (1–2 teaspoons) of vinegar or lime juice to reach desired creaminess and brightness.

Let the slaw rest for 10–20 minutes at room temperature to allow flavors to meld. For best texture and flavor, refrigerate covered for 30 minutes to 2 hours before serving. Toss again briefly before serving.

Adjust final seasoning to taste and serve chilled or at room temperature as a side, topping for tacos, sandwiches, or alongside grilled proteins.