Heat a tablespoon of olive oil in the skillet over medium heat. Add the diced sweet potato and cook, stirring occasionally, until they are tender and lightly browned, about 8 minutes.
Add the sliced onion to the skillet with the sweet potatoes, cooking until the onions are translucent and fragrant, about 3-4 minutes.
Stir in the chopped kale and chopped thyme, cooking until the kale wilts and reduces in volume, about 2-3 minutes. Season with salt and pepper to taste.
Meanwhile, in a mixing bowl, whisk the eggs until smooth. Stir in the shredded cheddar cheese.
Pour the beaten eggs evenly over the sautéed vegetables in the skillet. Give it a gentle stir to distribute everything evenly.
Transfer the skillet to a preheated oven set to 375°F (190°C). Bake until the eggs are puffed and set, about 15 minutes, and the top starts to turn golden.
Remove the skillet from the oven and let the frittata rest for a couple of minutes. Slice and serve warm to enjoy the vibrant colors and tender textures.