Warm the extra virgin olive oil in a large skillet over medium heat. Add sweet potato, onion, and season with salt and pepper, then toss to coat. Cover and cook for 5 minutes.
Remove lid, stir, and cook for another 2-3 minutes, stirring occasionally, so that the potatoes are lightly browned.
Add bell pepper and grape tomatoes to skillet and cook for another 3-4 minutes, stirring all the ingredients together frequently.
Clear out a section in the middle of the skillet (I like to form an X) and crack the four eggs into it, careful not to break the yolks. If desired, season tops of eggs with more salt and pepper. Cover and cook eggs until tops are opaque and yolks have reached the desired doneness. Egg cook times may vary per skillet and cooking unit, but in general: For a runny yolk, begin checking after 3 minutes and cook up to 6 minutes, doing a "shake test" (where you gently shake the pan to see the jiggliness of the eggs) every 30 seconds. For a firm yolk, begin checking after 5 minutes and cook up to 8 minutes, doing a "shake test" every 30 seconds.
Serve sweet potato hash immediately with chopped parsley as garnish (optional).
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