Preheat oven to 350°F. Arrange pecans in a single layer on a baking sheet. Toast, shaking pan once or twice, until golden brown and fragrant, 8 to 10 minutes. Let cool on a cutting board for 5 minutes, then coarsely chop.
Thinly slice Brussels sprouts crosswise into 1/4-inch rounds. Remove any woody stems that remain and, using your fingers, break up Brussels sprouts into thin ribbons.
Make dressing: Whisk cider vinegar, honey, mustard seeds, shallot, salt and pepper to taste.
In a large skillet, warm oil over medium heat. Add shredded Brussels sprouts; sauté, stirring, until soft but still retaining some crunch, about 5 minutes. Add dressing and cook, stirring to combine, for 1 to 2 minutes longer. Remove from heat. Toss apples and pecans with sprouts. Serve immediately.
Adapted with permission from Vibrant Food, written and photographed by Kimberley Hasselbrink (Ten Speed Press, copyright 2014).