Toss the salad. Combine the greens, apple, avocado, fennel, half of the pomegranate arils, walnuts, and half of the Parmesan in a large mixing bowl. Drizzle evenly with the shallot vinaigrette and toss gently until evenly combined.
Serve. Serve immediately, garnished with the remaining pomegranate arils and Parmesan and a few twists of freshly-ground black pepper. Enjoy!