Using a mandoline, a grater with 1 large hole, or a veggie peeler, peel the apple into thin shaves
Cut the greens on top of the fennel bulb off and toss. Using the same tool as you did for the apple, shave the fennel bulb until you have the desired amount of shaved fennel
Heat butter on a pan over medium heat. Once melted, add the walnuts and sprinkle with sugar. Stir walnuts to coat, and remove from the pan once toasted and caramelized (about 5 minutes)
Plate the salad with the apples, fennel, blue cheese, and walnuts. Drizzle with olive oil and sprinkle with salt & pepper.