How to Make It
Preheat oven to 425°F. Toss together broccoli florets, olive oil, garlic, salt, and crushed red pepper on a large rimmed baking sheet; spread in a single layer. Roast in preheated oven until broccoli is tender and edges are browned, about 20 minutes.
While broccoli roasts, heat 1 tablespoon oil in a medium skillet over medium. Add onion, and cook, stirring often, until onion is tender and beginning to brown, about 15 minutes. Stir in sliced broccoli stems and garlic, and cook, stirring occasionally, until broccoli is tender, about 8 minutes. Transfer stem mixture to a blender, and add vinegar, 1 tablespoon water, Dijon, salt, pepper, and remaining 1/3 cup oil. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process on high speed until smooth, about 1 minute.
To serve, transfer vinaigrette to a serving platter, spreading around platter with a spoon. Top with roasted broccoli mixture, and sprinkle with poppy seeds.