Preheat the oven to 400F and line a baking sheet with parchment. Place the squash on the baking sheet and drizzle it with oil. Sprinkle it with salt and pepper, then use your hands to mix everything. Transfer the squash to the oven and roast for 35 minutes, or until lightly browning at the edges. Alternately, you can use an air fryer and oil spray to cook the squash: 12-13 minutes at 375F, shaking the basket once through.
Trim the Brussels sprouts, then thinly slice them or use a mandolin to shave them.
To make the dressing, whisk all ingredients together till smooth. The leftover dressing can be stored in an airtight container for up to 5 days.
When the squash has finished roasting, allow it to cool for at least 20 minutes. Add it to a large mixing bowl, then add the Brussels sprouts and pomegranate arils, along with the vinaigrette. Toss to combine, then season to taste with additional salt and pepper as needed. Serve.
Notes
Leftover salad will keep for a day in an airtight container in the fridge.