Trim Brussels sprouts: slice off the root end and cut in half (cut them in thirds if they are very large). Toss with olive oil, salt, and pepper. Place cut side down on prepared baking sheet. Roast for 30-45 minutes, or until browned and crispy on the edges, stirring or shaking the pan occasionally to prevent burning. Cool slightly before adding to salad.
Assemble the salad: toss lettuce with apples, pecans, cheese, crumbled bacon, and Brussels sprouts. Toss with dressing.
Serve as soon as you add the sliced apples and dressing. To make ahead, assemble all but the apples and dressing and add those right before serving.
Prepare double the Brussels sprouts and bacon ahead of time: use them all week!