Place carrots into a large saucepan, pour in enough water to reach depth of 1 inch over carrots, and bring to a boil. Reduce heat to low, cover, and simmer carrots until tender, 8 to 10 minutes. Drain and transfer to a bowl.

Melt butter in the same saucepan; stir brown sugar, salt, cinnamon, and white pepper into butter until brown sugar and salt have dissolved. Transfer carrots into brown sugar sauce; cook and stir until carrots are glazed with sauce, about 5 more minutes. Transfer to serving bowl and toss with fresh thyme before serving.