1. Preheat the oven to 375 degrees . In a large bowl, whisk together eggs, egg whites, manchego and 1/4 teaspoon each salt and pepper.
2. Heat 1 tablespoon oil in a cast-iron skillet over medium heat. Add onion and cook, stirring occasionally, until golden, about 10 minutes. Add potato and cook, stirring occasionally, until slightly soft, about 5 minutes. Add garlic and cook 1 minute more. Add half the kale and cook 1 minute; add remaining kale and cook 2 minutes more. Add ham, remaining salt and pepper, and 1 tablespoon oil, then egg mixture, shaking pan to eliminate air pockets. Cook 1 minute on stove top, then transfer to oven and bake until lightly golden, 14 to 15 minutes.
3. Remove omelet from oven and let cool slightly. Meanwhile, toss greens with remaining oil and lemon juice. Serve with omelet.