Place carrots in a large pot and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender yet firm to the bite, 10 to 15 minutes. Drain and transfer to a serving bowl.
Combine brown sugar, butter, and bourbon together in a saucepan; bring to a simmer. Cook and stir sauce until thickened, about 10 minutes. Pour sauce over carrots and serve immediately.
