Preheat the Oven and Prepare the Baking Surface: Adjust the oven rack to the middle position and preheat your oven to 400°F (200°C). 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 Vegetables: Trim the dry ends off the Brussels sprouts. Halve or quarter them, depending on size, to ensure even cooking. Peel the sweet potatoes and cut them into uniform 1-inch cubes. Keeping the size of the pieces consistent is crucial for even cooking time.

Combine Vegetables and Seasoning: 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).

Toss Thoroughly: 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. Ensure the seasonings are distributed evenly throughout the bowl.

Arrange for Roasting: Spread the seasoned vegetables out onto the prepared baking sheet in a single layer. It is very important that the vegetables are not overcrowded; if they are layered on top of each other, they will steam instead of roast. If necessary, use two separate baking sheets.

Initial Roasting Period: Place the baking sheet into the preheated oven. 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.

Flip and Continue Roasting: 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.

Final Roasting and Check for Doneness: 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. The total cooking time should be between 30 and 35 minutes.

Serve: Remove the roasted vegetables from the oven. Taste and add an additional pinch of salt or pepper if desired. Serve immediately while they are hot.