Heat the oil in a cast iron (or other oven-proof) skillet over medium heat. Cook the onions until they begin to soften, 2 to 3 minutes.
Sprinkle in the kale and cook just until it wilts down, 1 to 2 minutes.
In a large bowl, beat the eggs with the salt. Pour egg mixture into the skillet. Sprinkle with Parmesan.
Place the skillet in the oven and bake until set, about 12 to 14 minutes. Sprinkle with pepper and serve. Leftovers are great reheated (or even cold in the lunch box)!