Add 3 tablespoons freshly squeezed lemon juice to a jar or small bowl.
Add 1 1/2 teaspoons Dijon mustard, 1 1/2 teaspoons granulated sugar, 1 small shallot, minced, and salt and pepper, to taste. Cover tightly and shake vigorously, or whisk with a fork until combined.
Slowly drizzle in 6 tablespoons extra virgin olive oil, then cover and shake again. Taste and add more sugar, salt, or pepper if needed. Set aside.
Add 12 ounces Brussels sprouts, trimmed to a food processor and pulse a few times to shred.
Bunch up 12 ounces kale, stems removed and julienne it finely.
Add 1/2 cup pine nuts to a dry skillet over medium-low heat and toast for 3 to 5 minutes, shaking the pan halfway through, until lightly golden. They burn quickly, so watch them closely. Set aside to cool. To toast them in the oven instead, spread the pine nuts on a baking sheet in a single layer and bake at 350 degrees F for 5 to 7 minutes, shaking the pan halfway through.
Add the shredded Brussels sprouts and chopped kale to a large salad bowl.
Pour the dressing over and toss to combine.
Add 2 apples, thinly sliced and 1 cup shaved Parmesan cheese and toss again.
Scatter the toasted pine nuts and 1/2 cup pomegranate arils over the top.
Serve right away, or let the salad rest for up to 30 minutes to soften the greens.
Notes
To make it ahead, keep the shredded greens, dressing, and toppings in separate containers, then combine just before serving.