Place carrots in a medium saucepan. Add water to cover by one inch. Bring to a boil. Partially cover and boil until tender crisp, about 5-8 minutes. Drain.
Heat olive oil in a large skillet over medium low heat. Add garlic and mushrooms and saute, stirring occasionally, until mushroom liquid evaporates, about 6 minutes.
Add carrots, sugar, thyme, salt and pepper, cover and cook over low heat 15 minutes. Uncover, remove garlic; discard. Increase heat to medium-high; cook, stirring often, until carrots and mushrooms are very lightly browned, 2-5 minutes.