Position a rack in the center of the oven and preheat the broiler. Whisk the eggs, 2 tablespoons water and the cayenne in a large bowl. Fold in the ham and half of the cheese.
Heat 1 tablespoon olive oil in an ovenproof 6-to-8-inch nonstick skillet over medium-high heat, swirling to coat the pan. Add the scallions, 1/4 teaspoon salt, and black pepper to taste; cook until soft, 4 to 5 minutes. Reduce the heat to medium low, pour in the egg mixture and stir gently with a rubber spatula to distribute the fillings. Cook until the bottom is just set, about 4 minutes. Sprinkle the remaining cheese on top, transfer to the oven and bake until puffed and golden, about 10 minutes. Let stand while you prepare the salad.
Season the tomato with salt and black pepper and toss with the vinegar, sugar and the remaining 3 tablespoons olive oil in a bowl. Add the greens and toss. Slice the pie and serve with the salad.