Preheat oven to 375 F. While the oven is preheating, prepare the Brussels sprouts by trimming off the end and removing the outer leaves. Thinly slice sprouts. To do this, I highly recommend using a food processor with the blade attachment.
Spread sliced Brussels sprouts into an even layer on a large baking sheet. Add half of the olive oil (about 2 tablespoons) and toss to evenly coat. Spread into a thin layer and roast in oven for 30 minutes. Halfway through the cooking time, add the pine nuts, stir, and spread out to an even layer. Remove from oven and allow to cool to room temperature. This can be made ahead up to this point and stored in the refrigerator in an airtight container until ready to serve.
Add roasted Brussels sprouts and toasted pine nuts to a large bowl. Add remaining olive oil, lemon juice and zest. Toss to evenly coat. Add almost all of the parmesan and pomegranate seeds, reserving some for the top. Add salt and pepper to taste (it may require up to a full teaspoon of salt to offset the bitterness of the sprouts and the tartness of the lemon).
Spoon into serving dish and top with reserved parmesan and pomegranate seeds.