Preheat oven to 425F. Line baking sheet with parchment paper.
Place chopped Brussels sprouts, sweet potatoes, onion, and garlic in a large mixing bowl. Drizzle the oil, salt, and peppers around the edge of the bowl, and toss to fully coat the vegetables.
Spread vegetables into a single layer onto the prepared baking sheet. Roast vegetables in the oven until Brussels sprouts are crisp, and the sweet potato is tender, about 20-25 minutes.
Heat a large nonstick pan over medium-high heat.
Add 1-2 tablespoons of olive oil and turn up to high heat. Add the sweet potatoes, brussels sprouts, onion, garlic, and salt and pepper. Let cook, stirring occasionally for about 4 minutes. (You may need to add a little water if the vegetables start to stick)
Make 4 “wells” with the back of a large spoon and crack the eggs into the hash. Cover and cook eggs until they reach desired doneness.
Take off the stove and sprinkle with optional ingredients.