Preheat the oven to 400˚. Heat the olive oil in a 10-inch nonstick ovenproof skillet over medium heat. Add the onion and cook, stirring often, until tender and slightly caramelized, about 10 minutes. Add the arugula and cook, stirring constantly, until wilted, 1 to 2 minutes. Reduce the heat to medium low.
Beat the egg whites and mustard in a medium bowl with a mixer on high speed until foamy.
Return the heat to medium and pour the egg white mixture into the skillet. Cook until the bottom is set, lifting the edges occasionally to allow the raw egg whites to drip to the bottom of the skillet, about 3 minutes. Top with the tomato slices and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Top evenly with the goat cheese.
Transfer the skillet to the oven and bake until the eggs are set, about 8 minutes. Drizzle with the balsamic glaze and a sprinkle of basil, if desired.