Preheat your oven to 425 degrees F. Prepare two sheet pans by lining them with foil and spraying with nonstick spray.
Cut the bottoms off the brussels sprouts and discard any brown outside leaves. Slice each sprout into thirds or quarters. Place sliced brussels sprouts on one of the pans, setting any loose leaves aside.
Wash, dry, and cut the bottom 2 inches off the asparagus. Place the asparagus on the other pan with the loose brussels sprouts leaves. (The asparagus and leaves cook quicker, so putting them together ensures that the leaves don't burn.)
Season both trays with salt, pepper, and olive oil.
Place the sheet pan with the brussels sprouts in the oven for 10 minutes before placing the sheet pan with the asparagus in the oven too. Cook both for 10 additional minutes or until the brussels sprouts are crisp and the asparagus is bright green and tender.
While the vegetables roast, add the sauce ingredients to a small mixing bowl and stir to combine.
To serve, remove vegetables from the oven and immediately scoop them onto a serving platter. Drizzle lemon tahini sauce over top. Then, sprinkle with pomegranate seeds and crushed pistachios. Garnish with chopped parsley.