How to Make It
Preheat the broiler. Set the tomatoes, cut side down, on a nonstick baking sheet and broil for 5 minutes. Remove the tomato skins and broil for another 2 minutes, or until just browned. Turn cut side up and broil for about 4 minutes, or until blackened. Transfer the tomatoes with any pan juices to a food processor and pulse until coarsely chopped. Add the shallots, balsamic vinegar and mustard. Season with salt and pepper and process until smooth. Transfer to a bowl.
In a small bowl, toss the Gruyère and Parmesan cheeses with 1/8 teaspoon each salt and pepper. Sprinkle in an even layer in a large nonstick skillet to form an 8-inch disk. Cook over moderate heat, spooning off the fat, until lightly browned, about 4 minutes. Using a spatula, carefully lift the crisp onto a paper towel-lined cookie sheet and blot dry.
Stir the chives into the dressing. Toss the greens with 6 tablespoons of the dressing; reserve the remaining dressing for another salad. Arrange the salad on 4 plates and crumble the cheese crisp on top.