Preheat your oven to 200°C (400°F) and line a large baking sheet with parchment paper.
Wash and dry the radishes and carrots. Trim the radishes and cut them in halves or quarters if large. Slice the carrots into uniform 1/2 inch sticks for even roasting.
Place the prepared vegetables in a large mixing bowl. Drizzle with 2-3 tablespoons of olive oil, then sprinkle generously with salt and pepper. Toss everything together until the vegetables are evenly coated with oil and seasonings.
Spread the vegetables out in a single layer on the prepared baking sheet. Make sure not to overcrowd the pan so they can roast evenly and develop a nice caramelized crust.
Roast in the oven for 25-30 minutes, flipping the vegetables halfway through. Look for golden edges and some slight charring, with a fragrant, sweet aroma filling your kitchen.
Check the vegetables for doneness; they should be tender and caramelized around the edges. If needed, roast for an additional 5-10 minutes to reach your desired softness and color.
Remove the vegetables from the oven. Drizzle with a teaspoon or two of vinegar or lemon juice for a bright, fresh contrast. Toss gently to distribute evenly.
Let the vegetables rest for a couple of minutes to allow flavors to meld. Garnish with fresh herbs if desired, and serve warm or at room temperature.