Preheat an oven to 425 degrees F (220 degrees C). Line a baking sheet with foil and spray with cooking spray.

Trim away root end, tough outer leaves, and dark green tops of leeks. Cut leeks lengthwise into quarters, then crosswise into thirds. Wash leeks well to remove any grit, and drain in a colander.

Melt butter in a large skillet over medium-high heat, and cook and stir leeks until they have started to soften, about 5 minutes. Sprinkle leeks with brown sugar, and cook until they turn brown, 15 to 20 minutes. Stir in matchstick carrots, sprinkle with kosher salt, and cook and stir until carrots are tender, about 5 minutes.

Place salmon on the prepared baking sheet, rub fillets with olive oil, and sprinkle with salt and pepper. Roast salmon until flesh is opaque and flakes easily but isn’t dry, about 10 minutes per 1-inch of thickness. Remove cooked fillets to plates, and top each fillet with 1/4 of the caramelized leeks and carrots.