Preheat your oven to 375°F (190°C).
Heat 1 tablespoon olive oil in a 10-inch oven-safe skillet over medium heat. Add sweet potato cubes and cook for 8-10 minutes until they begin to soften.
Add remaining olive oil and onion to the skillet. Cook for 3-4 minutes until onions become translucent.
Stir in garlic and kale. Cook until kale wilts, about 2-3 minutes.
In a large bowl, whisk together eggs, milk, salt, pepper, and red pepper flakes if using.
Spread vegetables evenly in the skillet and pour the egg mixture over them.
Sprinkle cheese on top and let cook on stovetop for 2-3 minutes until edges begin to set.
Transfer skillet to preheated oven and bake for 15-18 minutes, or until eggs are set and top is lightly golden.
Let rest for 5 minutes before slicing and serving.