In a large bowl, whisk mustard, 1/4 tsp. salt, a pinch of pepper and 2 Tbsp. lemon juice until salt dissolves. Slowly add oils, whisking until blended and thickened. Season with additional salt and pepper if desired. Stir in lemon zest.
Peel off tough outer layers of fennel bulb and cut in half. Remove tough core and thinly slice each half. (You should have about 6 cups, loosely packed.) Add to bowl with dressing.
Toss apple slices with remaining 1 Tbsp. lemon juice. Add to bowl along with cabbage and celery. Toss salad to coat all ingredients with dressing. Top with Parmesan shavings and serve.