Preheat oven to 425ºF. Line a large baking sheet with parchment paper.
Place brussels sprouts halves, shallots, and sage in a single layer on the parchment-lined baking sheet. Drizzle with olive oil, then sprinkle with 1/4 cup parmesan, salt, and pepper. Toss to coat evenly.
Bake for 20 minutes, then add the bread chunks, toss, sprinkle with another 1/4 cup parmesan, and continue to bake another 10 minutes.
Remove from the oven when edges are crispy and browning, sprinkle with red wine vinegar, toss, and sprinkle with remaining parmesan cheese and pomegranate seeds. Serve immediately.