Heat the olive oil in a large skillet over medium-high heat. Add the diced sweet potato, cover, and cook, stirring occasionally, for about 10 minutes, or until it begins to soften.
While the sweet potato cooks, dice the red onion and mince the garlic. Add to the skillet.
Dice and seed the bell peppers and add to the skillet.
Dice the jalapeño, if using, and add.
Chop the green onion and rosemary, if using fresh, and add to skillet. Cover and cook for about 5 minutes, or until the sweet potato is tender.
Create 4 wells in the vegetable mixture, not too close to the edges of the skillet, but far enough apart that they aren't touching. Crack 1 egg into each well. Cover and cook for 3-5 minutes more, or the eggs are cooked to your liking.