Preheat oven to 400 degrees.
Cut 4 pieces of parchment paper to 12 by 16 inches and arrange one fish fillet in the center of each. Season with salt and pepper and top with lemon slices and shallot. Drizzle with olive oil. To fold parchment, join long sides together and make a few 1/4-inch folds to seal. Fold ends like you're wrapping a gift and tuck underneath.
Transfer packets to a rimmed baking sheet. Bake until packet is puffed and fish is cooked through, 12 to 14 minutes. Remove from oven and let rest 5 minutes.
In medium bowl, whisk together tahini, lemon zest and juice, applesauce, and 1 tablespoon water. Season with salt.
Stir in broccoli, fennel, carrot, apple, and parsley until combined. Serve slaw with fish.