Preheat your oven to 425°F (220°C) and line a large baking sheet with parchment paper for easy cleanup.
In a large bowl, toss the diced sweet potatoes with 1 tablespoon of olive oil, a pinch of salt, and a dash of pepper. Spread them in a single layer on one side of the prepared sheet.
On the remaining side of the sheet, place the halved Brussels sprouts. Drizzle with the remaining tablespoon of olive oil, and season with salt, pepper, paprika, and thyme. Toss gently so everything is evenly coated.
Roast for 15 minutes, then give the pan a quick stir to promote even browning. If you’re adding onions, scatter them over the sheet now and roast for another 10–12 minutes until both the potatoes are tender and the sprouts are caramelized around the edges.
While the veggies roast, heat a large skillet over medium heat. If you’d like, add a splash of oil and sauté the minced garlic for about 30 seconds until fragrant, being careful not to burn it. If using onions in the roast, you can skip this step.
Remove the tray from the oven. The potatoes should be tender and the Brussels sprouts nicely browned. If they need a little more color, return to the oven for 3–5 minutes, watching closely.
Transfer the roasted vegetables to the skillet with the garlic. Toss gently to combine. If you’re adding lemon juice or balsamic, drizzle it over now and season to taste with salt and pepper.
Optionally, top with grated parmesan or feta for a savory finish and scatter fresh herbs over the top.
If you’re serving with eggs, prepare them to your liking (soft-poached, sunny-side up, or scrambled) and place them atop the hash just before serving. For a study-friendly brunch, this hash also shines with a fried egg perched on top.
Taste and adjust seasoning. A squeeze of lemon or a splash of vinegar brightens the dish beautifully, balancing the sweetness of the roasted potatoes.