Preheat oven to 425°F. Line a large rimmed baking sheet with foil and coat with cooking spray.
Combine 3 tablespoons mayonnaise and 1 teaspoon chili powder in a small bowl. Set aside.
Toss 2 sweet potatoes with 2 teaspoons oil, ¼ teaspoon salt and ⅛ teaspoon pepper in a medium bowl. Spread on the prepared baking sheet. Roast for 15 minutes.
Meanwhile, toss 4 cups broccoli with the remaining 2 teaspoons oil, ¼ teaspoon salt and ⅛ teaspoon pepper in the same bowl. Remove the baking sheet from oven. Stir the sweet potatoes and move them to the sides of the pan. Arrange 1¼ pounds salmon in the center of the pan and spread the broccoli on either side, among the sweet potatoes. Spread 2 tablespoons of the mayonnaise mixture over the salmon. Bake until the sweet potatoes are tender and the salmon flakes easily with a fork, about 15 minutes.
Meanwhile, add lime zest and lime juice from 1 lime to the remaining 1 tablespoon mayonnaise; mix well.
Divide the salmon among 4 plates and top with ¼ cup cheese and ½ cup cilantro. Divide the sweet potatoes and broccoli among the plates and drizzle with the lime-mayonnaise sauce. Serve with lime wedges and any remaining sauce.
