Preheat your oven to 220°C (430°F). Line a baking sheet with parchment paper to prevent sticking and make cleanup easier.
Peel the carrots if desired, then cut them into uniform 1-inch sticks. Trim the asparagus, removing the woody ends, and set aside.
In a large mixing bowl, toss the carrots and asparagus with 2 tablespoons of olive oil, ensuring each piece is evenly coated. Season generously with salt and freshly cracked black pepper.
Spread the vegetables in a single layer on the prepared baking sheet, giving each piece space for proper caramelization.
Roast in the oven for 20 minutes, until they start to turn golden and fragrant. During this time, the vegetables will begin to caramelize and develop smoky edges.
After 20 minutes, use tongs to flip the vegetables for even browning, then continue roasting for another 10-15 minutes until tender and crispy at the edges.
Remove the vegetables from the oven and transfer to a serving dish. Squeeze fresh lemon juice over the top to add brightness and balance the smoky sweetness.
Garnish with fresh thyme or rosemary sprigs if desired, then serve warm for a beautifully caramelized, smoky vegetable side.
