Peel and chop sweet potato into approximately 1/4-inch cubes. Chop and de-stem kale.
Over medium-high heat place 2 tbsp olive oil in a large skillet with a lid. After oil is hot (about 2 minutes) place chopped sweet potato in the skillet. Using a spatula, toss the sweet potatoes until they are all coated in oil. Cover for about 1 minute, then check the sweet potatoes and move around in the pan, watching to make sure they don’t get too brown. If they are sticking, add more oil. Repeatedly cover the potatoes for about a minute at a time and check them for doneness and adjusting heat as necessary. Use spatula to push check sweet potato for softness. They are done when the outside is slightly browned and they are soft on the inside.
Add kale to the pan and about 1 tbsp extra oil. Stir kale until coated with oil. Reduce heat to low.
Create four “wells” in the sweet potato/kale mixture and add a small amount of oil to each well. Cover the pan and keep the heat on low. After about 3.5 minutes, the eggs will be cooked to over medium, with cooked whites and runny yolks. At this point, remove from heat. Salt to taste and enjoy!
Use a bit more oil with each step to prevent sticking and burning.