Arrange the pecans in a single layer on a baking sheet. Toast until golden brown and fragrant, about 8 to 10 minutes. Set aside to cool for about 5 minutes, then coarsely chop.
Thinly slice the brussels sprouts crosswise into 1/4 inch rounds. Remove any of the woody stem that remains and using your fingers, break up the sprouts into thin ribbons. Set aside.
To prepare dressing, whisk together the cider vinegar, honey, mustard seeds, shallot, salt and pepper to taste. Set aside.
In a large skillet over medium heat, warm the oil. Add the shredded brussels sprouts and saute, stirring, until soft but still retaining some crunch, about 5 minutes. Add the dressing and cook for 1 to 2 minutes longer, stirring to combine. Remove from the heat to avoid wilting the sprouts. Toss the apples and pecans with the sprouts. Serve immediately.