Finely dice the red onion into 1/8-inch pieces and set aside—this size is crucial so the onion flavor distributes evenly without overpowering the dressing. Finely chop the parsley and set aside. Shred the green and red cabbage into 1/8-inch wide strips using a sharp knife or mandoline, keeping them separate or combined as you prefer. Grate the carrots into thin shards. I find that getting consistent vegetable sizes ensures even flavor distribution and the best texture throughout the slaw.

In a large mixing bowl, combine the mayonnaise, lemon juice, apple cider vinegar, sugar, salt, pepper, Dijon mustard, and celery seed. Whisk together until the sugar dissolves completely and the dressing is smooth and well-emulsified. The vinegar and lemon juice will help break down the sugar, but take 30-45 seconds to ensure it's fully incorporated for a balanced flavor.

Add the shredded cabbage, grated carrots, diced red onion, and chopped parsley from Step 1 to the dressing base from Step 2. Using a large spoon or rubber spatula, gently fold everything together until all the vegetables are evenly coated with the dressing. I like to be thorough but gentle here—you want every piece of vegetable coated, but you're not trying to break down the cabbage. Make sure there are no dry pockets of vegetables.

Cover the bowl with plastic wrap or a lid and refrigerate for at least 2 hours. This resting time allows the vegetables to soften slightly, the flavors to meld together, and the dressing to be fully absorbed by the cabbage. The longer it sits (up to 24 hours), the more developed and cohesive the flavor becomes.

Remove the coleslaw from the refrigerator and give it a good stir to redistribute the dressing and ensure even coating. Taste for seasoning and adjust salt, sugar, or vinegar to your preference. Serve cold as a side dish alongside pulled pork, barbecue, or any sandwich.