Crack the eggs into a large bowl, add salt and pepper and beat well with a fork.
Place 2 teaspoons oil in an ovenproof nonstick pan over medium heat. Add the sweet potatoes and cook for 8 - 10 minutes, add the onion and garlic and sauté until tender 1 - 2 minutes. Add the kale and thyme cook for another minute, until kale has just wilted.
Pour the beaten eggs into the skillet and cook for 3 - 4 minutes. Crumble the goat cheese over the top, then place the pan in the oven and bake until the center is set and lightly golden, about 20 - 25 minutes.