Start by prepping your vegetables with clean, sharp knives for safety and consistency. Shred the green and red cabbage into thin, uniform ribbons and place them in a large mixing bowl.
Core your three medium apples and julienne them into matchstick-sized pieces to match the cabbage texture. Toss the apple pieces immediately with 1 tbsp of lemon juice to prevent browning and add brightness to the mix.
In a separate small bowl, whisk together your dressing: apple cider vinegar, honey, Dijon mustard, Greek yogurt, remaining lemon juice, and olive oil. Season with sea salt, black pepper, and caraway seeds, stirring for 1-2 minutes until completely smooth.
Pour this cozy apple slaw side recipe dressing over the cabbage and apple mixture, then gently fold everything together with a wooden spoon. Make sure every strand gets coated evenly, working carefully to avoid bruising the delicate vegetables.
Stir in your chopped fresh parsley, dried cranberries, and toasted walnuts, folding gently for about 30 seconds until the slaw feels cohesive. Let the salad rest for 5-10 minutes before serving so flavors can meld and soften.