Preheat your oven to 450°F. While it heats, prepare the vegetables: halve the brussels sprouts through the core (this cut exposes the flat sides that will caramelize beautifully) and peel the carrots, then slice them into 1/2-inch thick rounds. Arrange your vegetables on a parchment-lined baking sheet in a single layer, ready for seasoning.

In a small bowl, combine the salt, pepper, garlic powder, and paprika to create your seasoning blend. Drizzle the olive oil over the prepared vegetables on the baking sheet, then sprinkle the seasoning mixture evenly over everything. Toss gently with your hands or two spoons until all the vegetables are well coated with oil and seasoning. I like to make sure every brussels sprout half has its flat side down on the pan—this direct contact with the hot sheet is what creates that crispy, caramelized exterior.

Place the baking sheet on the bottom rack of your preheated 450°F oven. Roast for 15 minutes without disturbing the vegetables—the bottom rack and direct contact with the sheet will help develop deep browning on the cut sides of the brussels sprouts and caramelize the carrots.

After 15 minutes, flip all the vegetables over and move the baking sheet to the middle rack. This allows the other sides to brown while ensuring more even cooking. Roast for 7 to 15 minutes longer until the vegetables are golden brown and the brussels sprout edges are deeply caramelized and crispy. The timing depends on the size of your pieces and how caramelized you like them—start checking at 7 minutes. I always taste a piece to make sure they're cooked through and have that wonderful roasted flavor before serving.

Remove the pan from the oven and transfer the roasted vegetables to a serving dish. Taste a piece and adjust seasoning if needed—you can add a drizzle of extra olive oil and a pinch of salt or garlic powder if desired. Serve immediately while the vegetables are still warm and crispy.