Scrub the carrots and trim the tops. If some carrots are thicker, cut them into halves or fourths (lengthwise) so that all carrot pieces are approximately the same diameter.
Toss the carrots with extra-virgin olive oil so that they are evenly coated.
Spread the carrots on the roaster and evenly sprinkle them with garlic, salt and pepper. Toss several sprigs of fresh thyme on top (retain a sprig or two of thyme for garnish).
Roast, stirring every 5 minutes, for 20 to 30 minutes total, or until the carrots are very tender and starting to caramelize around the edges. Remove the cooked thyme stems. Adjust the seasonings with additional pepper.
Transfer the carrots to a serving platter, sprinkle with additional chopped fresh thyme leaves and serve immediately.