Preheat the oven to 450 degrees F. Slice (shave) the brussels sprouts very thin and divide equally onto two large rimmed baking sheets. Drizzle each pan with 1 tablespoon of olive oil. Salt and pepper the shaved brussels sprouts liberally. Then toss to coat and spread out evenly over each baking sheet. Roast in the oven for 15 minutes. Flip the shaved Brussels and spread out again. Then continue roasting for another 15-25 minutes until the edges are crispy.
Meanwhile, place the remaining 4 tablespoons of olive oil in a glass jar and add the vinegar, maple syrup, and mayonnaise. Screw the lid on the jar and shake vigorously until smooth. Salt and pepper the dressing to taste.
Once the Brussels sprouts and maple vinaigrette are ready, slice the apples into paper-thin wedges. Distribute the crispy Brussels sprouts onto four plates and top with apple slices, walnuts, and dried cranberries. Drizzle each salad with maple vinaigrette and serve while the roasted Brussels sprout salad is still warm.