Preheat your oven to 220°C (425°F) and line a large baking sheet with parchment paper.
Wash and trim the radishes, then cut them in halves or quarters depending on size. Peel the carrots and slice them into uniform sticks or rounds for even roasting.
Place the prepared radishes and carrots into a mixing bowl, then drizzle with olive oil. Toss gently to coat all pieces evenly, ensuring they’re slightly slick but not swimming in oil.
Add a pinch of flaky sea salt, a few sprigs of fresh thyme, and sprinkle smoked paprika if using. Toss again to distribute the seasonings evenly.
Spread the seasoned vegetables in a single layer on your prepared baking sheet, making sure they aren’t crowded so they caramelize properly.
Roast in the oven for 20-25 minutes, shaking the pan or flipping the vegetables halfway through to promote even browning and caramelization.
Watch for deep golden edges and tender texture when pierced with a fork, indicating they are perfectly roasted.
Remove the vegetables from the oven and let them rest for a few minutes. Drizzle with a splash of balsamic vinegar or sprinkle toasted sesame seeds for extra flavor if desired.
Serve warm directly from the baking sheet or transfer to a serving platter. Enjoy their smoky, tender sweetness with any main dish or as a hearty side.