Begin by preheating your oven to 375°F (190°C). While it warms up, peel and dice the sweet potatoes into small cubes—smaller pieces cook faster and evenly.
Heat the olive oil in your oven-safe skillet over medium heat. Add the diced sweet potatoes and cook for about 8-10 minutes, stirring occasionally, until they start to soften and develop a light golden color. Add the chopped onion and continue cooking until the onion becomes translucent and the sweet potatoes are fork-tender.
Add the chopped kale to the skillet and sauté for an additional 2-3 minutes, until it softens and reduces in volume. This step infuses the kale with the flavors of the sweet potatoes and onions, creating a harmonious base for the frittata.
While the veggies cook, whisk together the eggs, milk, salt, and black pepper in a mixing bowl until frothy. The milk helps create a tender texture, while seasoning ensures every bite is flavorful.
Pour the egg mixture evenly over the sautéed vegetables in the skillet. Sprinkle the shredded cheese on top, allowing it to melt into the eggs and veggies as the frittata bakes.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the eggs are set and the top is lightly golden. You can test doneness by gently shaking the pan; the center should no longer jiggle.
Remove the skillet from the oven and let the frittata cool for a few minutes before slicing. This resting time helps it firm up and makes serving easier. Pair it with a fresh salad or a side of your favorite roasted potatoes for a complete meal.