Preheat the oven to 400°F (204°C) and line a large rimmed baking sheet with parchment paper.
In a large mixing bowl, combine the broccoli florets and carrot coins.
Drizzle the oil over the vegetables and add the minced garlic, salt, pepper, and dried thyme.
Toss thoroughly until the vegetables are evenly coated with the oil and seasonings.
Spread the vegetables in a single layer on the prepared baking sheet, ensuring they are not overcrowded to allow for proper roasting.
Roast in the center of the oven for 20 to 25 minutes, tossing halfway through, until the carrots are fork-tender and the broccoli edges are browned.
Remove from the oven and serve immediately.