Heat the oven to 450°. Put the oil in a small stainless-steel, enameled, or nonstick roasting pan and heat in the oven for 5 minutes. Season the fish with 1/2 teaspoon salt and 1/4 teaspoon pepper. Put the fish in the hot pan; cook in the oven until just done, about 8 minutes. Push the vegetables to the edges of the pan and place the salmon in the center. Season vegetables with salt and pepper.
Remove the fish from the pan and transfer to paper towels to drain. Pour off any oil remaining in the pan. Put the pan over moderate heat and add the wine and the chopped vegetables. Bring to a boil, scraping the bottom of the pan to dislodge any brown bits. Cook until the wine is reduced to approximately 3 tablespoons, 1 to 2 minutes.
Reduce the heat to low and whisk in the butter. Season the sauce with a pinch each of salt and pepper. Put the fish on plates, browned-side up. Serve with roasted carrots and Eggplant. Spoon the sauce over the fish.