How to Make It
In a small bowl, combine 2 tablespoons of the olive oil with the lemon juice, vinegar and 1/4 teaspoon each of salt and pepper.
In a large skillet, heat 1 tablespoon of the olive oil. Add the chanterelles and 1 tablespoon of the butter and season with salt and pepper. Spread the mushrooms in an even layer and cook over moderately high heat, without stirring, until deeply browned on the bottom, about 4 minutes. Stir the mushrooms and continue cooking until tender, about 3 minutes longer. Transfer to a plate.
Return the skillet to high heat and add the remaining 1 tablespoon of oil. Season the scallops with salt and pepper. When the oil is hot, add the scallops to the skillet along with the remaining 1 tablespoon of butter; tilt the pan to coat the undersides of the scallops with butter. Cook, without stirring, until the scallops are deep brown on the bottom, about 3 minutes. Turn the scallops and cook until browned on the second side and just cooked through, about 3 minutes longer.
In a medium bowl, toss the arugula and fennel with 3 tablespoons of the dressing. Transfer the salad to 2 large plates. Add the tomatoes and mushrooms to the bowl and toss with the remaining dressing; arrange over the salads along with the scallops. Shave thin slices of Parmesan cheese on top and season with pepper. Drizzle with truffle oil and serve at once.