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Preheat oven to 400°. Toss broccoli and 2 Tbsp. oil on a large rimmed baking sheet; season with salt and pepper. Roast, tossing occasionally, until browned and crisp-tender, 12–15 minutes.
Remove baking sheet from oven and rub salmon with 1 Tbsp. oil; season with salt and pepper. Push broccoli to edges of baking sheet and place salmon in the center. Roast until salmon is opaque throughout, 10–15 minutes.
Meanwhile, combine chile, vinegar, and a pinch of salt in small bowl and let sit until chiles are slightly softened, about 10 minutes. Mix in capers and remaining 1 Tbsp. oil; season with salt and pepper.
Serve salmon and broccoli drizzled with chile vinaigrette.
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