Preheat your oven to 375°F (190°C). Position the rack in the middle of the oven.
Heat a 10-inch oven-safe skillet over medium heat. Add 1 tablespoon olive oil and sweet potato cubes. Cook for 8-10 minutes, stirring occasionally, until they're nearly tender. Pro tip: cover the pan for the first 5 minutes to help them cook faster.
Add the remaining oil, onions, and garlic. Cook until the onions become translucent, about 3-4 minutes.
Toss in the kale and cook until it wilts, about 2-3 minutes. Season with a pinch of salt and pepper.
While the vegetables cook, whisk together eggs, milk, half the cheese, ½ teaspoon salt, and ¼ teaspoon pepper in a bowl.
Pour the egg mixture over the vegetables, giving everything a gentle stir to distribute evenly. Let it cook undisturbed for 3-4 minutes until the edges start to set.
Sprinkle the remaining cheese on top and transfer the skillet to the preheated oven.
Bake for 12-15 minutes, or until the eggs are set and the top is lightly golden.