Preheat the oven to 450°F (230°C).
Cut the broccoli into approximately 2-inch florets. Slice the remaining tender broccoli stem crosswise into roughly 1-inch pieces.
Add the broccoli, butternut squash, Brussels sprouts, and red onion to a large rimmed baking sheet. Drizzle with olive oil and season with salt and black pepper. Toss until everything is evenly coated.
Spread the vegetables into a single layer. Place the squash toward the outer edges of the baking sheet and arrange the other vegetables closer to the center. Position the Brussels sprouts cut side down when possible.
Roast without stirring for 20 to 25 minutes, or until the vegetables begin to shrink and develop browned, caramelized edges.
While the vegetables roast, finely grate or mince the garlic into a small bowl. Add the Dijon mustard and maple syrup and stir until smooth.
Remove the baking sheet from the oven. Sprinkle the pecans or walnuts over the vegetables, if using, and drizzle the maple-Dijon mixture evenly over everything.
Toss gently with a spatula until the vegetables and nuts are coated, then spread them back into an even layer.
Return the Maple Dijon Roasted Vegetables to the oven and roast for about 10 minutes more, until the butternut squash is fork-tender, the vegetables are caramelized in spots, and the nuts smell toasted and fragrant.
Toss once more before transferring to a serving platter. Serve warm