Preheat the oven to 400 degrees.
Slice the stalks from the fennel bulb, reserving the fronds for the salad. Cut in half lengthwise; then slice into long, thin wedges lengthwise.
Toss the fennel with 1 tablespoon olive oil and spread onto a baking sheet. Roast until the fennel is cooked through and browning around the edges, flipping once halfway through, 25-30 minutes.
While the fennel is roasting, prepare the remaining ingredients. Core and thinly slice the apples, using a mandoline or sharp chef’s knife. Thinly slice the radicchio, then transfer to a salad bowl along with the fennel fronds. Add the roasted fennel to the salad along with the lemon zest, lemon juice, remaining olive oil and season with salt and pepper to taste. Toss well to combine and top with shaved cheese.