Heat oven to 425° F with a rack positioned in the upper third. Toss the broccoli, garlic, chili, 2 tablespoons of the oil, 1 teaspoon salt, and ½ teaspoon pepper on a rimmed baking sheet.
Nestle the salmon in the broccoli and season with ¼ teaspoon each salt and pepper.
Roast, tossing the broccoli once, until the salmon is just opaque but still slightly pink in the center and the broccoli is crisp-tender, 15 to 20 minutes. Flake the salmon into large chunks.
Meanwhile, cook the quinoa according to package directions.
Whisk the vinegar, soy sauce, and the remaining 2 tablespoons of oil in a small bowl.
Serve the salmon and broccoli over the quinoa, topped with the peanuts and the soy-vinegar sauce.