Preheat your oven to 375°F (190°C).
In a medium mixing bowl, whisk together the whole eggs, egg whites, sea salt, black pepper, and garlic powder until well combined and slightly frothy.
Heat the extra virgin olive oil in a 10-inch oven-safe non-stick or cast-iron skillet over medium heat.
Add the thinly sliced shallot to the skillet and sauté for 2-3 minutes until translucent and fragrant.
Add the baby arugula to the skillet and toss briefly for about 30 seconds until it just begins to wilt.
Pour the egg mixture into the skillet over the shallots and arugula, ensuring the greens are evenly distributed.
Allow the eggs to cook undisturbed for 2 minutes on the stovetop until the edges begin to set.
Sprinkle the crumbled goat cheese evenly over the top of the egg mixture.
Transfer the skillet to the preheated oven and bake for 12-15 minutes, or until the center is set and the top is lightly golden.
Remove from the oven, let rest for 5 minutes, then slice into wedges and serve.