Preheat the broiler. Place the bread on a baking sheet and broil until lightly golden on both sides.
Whisk 2 tablespoons olive oil with the garlic and basil in a small bowl; brush evenly on the toasted bread. Season the tomatoes with salt and pepper; arrange a layer of tomatoes on each bread slice. Chop any remaining tomato slices and set aside for the salad. Top the bread evenly with the gruyere, mozzarella and parmesan. Return to the broiler and cook until the cheese melts, about 2 minutes.
Whisk the vinegar and the remaining 2 tablespoons olive oil in a large bowl; season with salt and pepper. Add the greens and the reserved chopped tomatoes and toss. Serve the cheese toast with the salad and chips.