Preheat oven to 400 degrees (you will use it to bake the eggs into the skillet at the very end)
Heat a large skillet, (preferrably cast iron or oven-safe) over medium heat and add 1 tbsp of the oil. Add the onions and peppers cook until the onions and peppers are soft and fragrant. Remove from heat and set aside until the potatoes are done.
Meanwhile in a separate skillet over medium heat, add the remaining oil and chopped sweet potatoes and stir to coat. Sprinkle with sea salt and pepper to taste.
Cook and stir, uncovered, until the outside begins to brown, then cover the skillet (any cover that mostly fits will do!) and continue to cook to soften the inside of the potatoes, uncovering to stir once in a while. Adjust the heat if necessary to prevent burning, and add a bit more oil if necessary. This step should take about 7 minutes total, give or take.
Once the potatoes are softened and browned, transfer them to the onion and pepper skillet and stir to combine. Create 4 indents where you will crack each egg - then carefully crack the eggs into the spaces (I like to create a bit of space for the eggs so the yolks don't break and the whites don't run all over!)
Put the entire skillet in the 400 degree oven to bake the eggs to preference, about 10-15 minutes. Alternatively, you can cook the eggs by covering the skillet and cooking over medium-low heat until the eggs are done.
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