Preheat oven to 400°F and line a large, rimmed baking sheet with parchment paper or a baking mat. Set aside.
Toss broccoli with 1½ tablespoons olive oil in a large bowl and season with salt and pepper, to taste. Transfer to a prepared baking sheet and spread broccoli into a single layer without overcrowding. Place in preheated oven and roast for 12-15 minutes or until tender and starting to brown. Remove from the oven and set aside.
While broccoli is roasting, heat remaining olive oil in a large skillet over medium-high heat. Add onion and sauté, stirring occasionally, until tender, approximately 5 minutes.