With the rack in the middle position, preheat the oven to 200 °C (400 °F).
In a skillet, brown the vegetables with the garlic and bay leaf in the butter. Season with salt and pepper. Add the broth and bring to boil. Bake, uncovered, for about 45 minutes or until the vegetables are tender. Keep warm.
In a large non-stick skillet, brown the fish on both sides in the butter and oil and cook until the desired doneness. Season with salt and pepper.
Place the vegetables in four shallow bowls. Top with the fish. In a blender or with an immersion blender, froth the leek and basil milk with the remaining butter. Adjust the seasoning. Drizzle the frothed milk on the vegetables and fish.