Special equipment: a straight-sided 3-quart tall glass bowl or four 16-ounce wide-mouth glass jars with lids
Preheat the oven to 350 degrees F. Spread the pecans out on a baking sheet, and roast until golden, 8 to 10 minutes. Let cool, and roughly chop. Turn the oven up to 425 degrees F. Transfer the pecans to a medium bowl. Add 1/3 cup vinegar, the mustard, honey, 1/2 teaspoon salt and a few grinds of black pepper, and whisk to combine. Slowly drizzle in the oil while whisking constantly until blended into a vinaigrette.
Spread the sweet potatoes out on a rimmed baking sheet. Drizzle with 3 tablespoons of the vinaigrette, sprinkle with a large pinch of salt and toss to combine. Roast until the squash is fork-tender and browned in spots, 30 to 40 minutes. Remove and let cool. (The sweet potatoes can be made and refrigerated up to 2 days ahead.)
Meanwhile, bring a medium pot of water to a simmer, add the wheat berries and cook until tender, 20 to 30 minutes. Let cool in the pan. (The wheat berries can be made and refrigerated up to 2 days ahead.)
Put the cabbage in a medium bowl, and add the remaining 2 tablespoons vinegar and 1/4 teaspoon salt. Rub the vinegar and salt into the cabbage, and let sit until tender, about 30 minutes, tossing and massaging again about halfway through.
Using a 3-quart tall glass bowl for 1 large salad or four 16-ounce wide-mouth glass jars with lids for individual salads, make a first layer with the wheat berries, then add the following in separate layers: half the cabbage, the sweet potatoes, Cheddar, parsley and peppers, the remaining cabbage, the ham and kale. Top with the apple chips. (The salad, except for the apple chips, can be put together, covered and refrigerated for up to 2 hours; top with the chips right before serving.)
If making 1 salad, just before serving, transfer it to a large bowl, toss with the dressing and season with salt and pepper. If making 4 salads, add dressing to each jar, season with salt and pepper, cover with the lid and shake to coat.
To achieve pretty, defined layers, be sure to layer more on the sides. It's OK if there isn't enough of an ingredient to fill the middle.