Position a rack on the shelf closest to the grill, and preheat the grill to high heat.
Toss the tomatoes with the vinegar, and 1 teaspoon of the olive oil. Season with salt and pepper; set aside.
Warm a medium nonstick frying pan (grill safe) over medium-low heat. Whisk the egg whites in a large bowl until foamy and doubled in volume; season with salt and pepper and whisk in the parsley. Add the remaining 2 teaspoons olive oil to the skillet. Pour the whites into the skillet and swirl to cover entire pan. Cook, without stirring, until the whites are almost set and light brown on the bottom, about 3 minutes.
Transfer the pan under the grill and cook until the omelette sets and begins to brown, about 30 seconds. Spoon half of the tomato salad onto half of the omelette and fold the omelette over the filling. Transfer omelet to a serving platter and scatter the remaining tomato salad on top. Serve with the baby greens on the side.