Preheat your oven to 400°F (200°C) and adjust the oven rack to the middle position. Line a large, heavy-duty rimmed baking sheet with parchment paper or aluminum foil for easier cleanup. If using foil, lightly spray it with cooking oil.

Prepare the Brussels sprouts by trimming the dry ends and halving them lengthwise (or quartering very large sprouts). Peel the sweet potatoes and cut them into uniform 1-inch cubes. Consistency in size is crucial for even cooking.

In a very large bowl, combine the cut Brussels sprouts and the cubed sweet potatoes. Drizzle the 3 tablespoons of olive oil over the vegetables. Add the kosher salt, black pepper, garlic powder, and dried thyme (if using).

Using your hands or a large sturdy spoon, toss the mixture vigorously until every piece of vegetable is thoroughly coated in the olive oil and seasoning mixture.

Spread the seasoned vegetables out onto the prepared baking sheet in a single layer. It is critical that the vegetables are not overcrowded; use two baking sheets if necessary to ensure they roast and do not steam.

Place the baking sheet into the preheated oven and roast for 15 minutes. The edges of the sweet potatoes should just begin to look tender, and the bottoms of the Brussels sprouts should start to brown.

After 15 minutes, remove the baking sheet from the oven. Using a spatula, thoroughly flip and toss the vegetables so that the other side of the pieces is exposed to the hot pan surface. Return the baking sheet to the oven.

Continue roasting for another 15 to 20 minutes, or until the sweet potatoes are fork-tender and the Brussels sprouts are deeply golden brown and crispy at the edges (total cooking time 30–35 minutes). Taste, adjust seasoning if necessary, and serve immediately.