In a large bowl, combine the shredded cabbage, broccoli slaw mix, carrots, and scallions. Toss everything together gently to distribute the vegetables evenly. This is your vegetable base—keeping these ingredients separate from the dressing for now allows them to stay crisp and prevents the coleslaw from becoming soggy.
In a separate bowl, whisk together the yogurt, mayonnaise, vinegar, lemon juice, minced garlic, salt, and white pepper until smooth and well combined. The yogurt and mayo create a creamy base while the vinegar and lemon juice add brightness and acidity. I like to taste the dressing at this point and adjust the seasoning—a little extra salt can really help bring out all the flavors.
Just before serving (no more than 20 minutes ahead), core the apple and cut it into thin 1/4-inch matchsticks. Add the fresh apple and the dressing from Step 2 to the vegetable mixture from Step 1, then toss everything together until the vegetables are evenly coated. The timing here is important—I wait until the last minute to add the apple so it stays crisp and doesn't turn brown or absorb too much moisture from the dressing.