Preheat the oven to 350°F (175°C). Cook the rice according to package instructions.
Meanwhile, heat the olive oil in a large skillet. Add the sunchokes and cook, stirring occasionally, until softened, about 10 minutes. Add the butternut squash and leeks and cook for about 10 minutes more.
Transfer the vegetables to a 9 x 13-inch baking pan. Stir in the cooked rice and salmon.
Wipe out the skillet and melt the butter. Add the garlic and cook 30 seconds, until fragrant.
Stir in the flour until the mixture has thickened. Slowly pour in the wine, whisking continuously. Simmer for about 2 minutes until the wine has reduced in half.
Gradually pour in the milk, whisking continuously. Simmer for a couple of minutes until the sauce starts to thicken.Stir in the Parmesan cheese, until melted. Finally, add the salt, black pepper, oregano, thyme, and cayenne pepper and stir well.
Pour the sauce over the vegetables, rice, and salmon and stir everything together. Bake for 30 minutes.