In a medium-sized cast iron skillet over medium-high heat, add the olive oil. Once hot and shimmering, add the onion and garlic and saute for 2 minutes, or until the onion begins to soften and the garlic becomes fragrant.
Add the sweet potato and Brussels sprouts, sprinkle with salt and pepper, and stir gently to coat. Turn the heat to medium and cover for 5 minutes, stirring once.
Remove the cover and continue to cook until the sweet potatoes and Brussels sprouts brown, around 10 minutes, stirring occasionally.
Sprinkle in the shiitake mushroom bacon and stir gently to combine. Create two small nests for the eggs, then crack one egg into each. Cover and allow to cook for around 5 minutes, or until the whites have set.
Remove from heat, sprinkle with additional salt and pepper if needed, and serve immediately.