Bring a pot of well-salted water to a boil. Set up a bowl of well-salted ice water. Blanch the carrots in the boiling water. When they are cooked but still have some crunch, plunge them immediately into the ice water. When cool, use a clean tea towel to rub the skin off the carrots. Reserve.
To a large skillet add the butter, sugar, lemon juice, garlic, thyme, cayenne and about 1/2 cup of water. Bring the pan to medium heat swirling occasionally. When most of the water has reduced and the mixture seems homogenous, removed the garlic and add the carrots and stir until they are coated. Cook for another 2 to 3 minutes or until the carrots are completely coated and hot.