Slice the carrots, on the bias, about 1/4 inch thick.
Bring the carrots, salt, 1 tablespoon of the sugar, and the chicken broth to a boil in a 12-inch skillet, covered, over medium-high heat. Reduce the heat to medium and simmer, covered, stirring occasionally, until the carrots are almost tender when poked with a fork, about 5 minutes. Uncover, increase the heat to high, and simmer rapidly, stirring occasionally, until the liquid is reduced to about 2 tablespoons, 1 to 2 minutes.
Cut the butter into 4 pieces and add it to the skillet along with the remaining 2 tablespoons sugar. Toss the carrots to coat and cook, stirring frequently, until the carrots are completely tender and the glaze is light gold, about 3 minutes. Off the heat, add the lemon juice and minced thyme and toss to coat.
Season to taste with pepper and serve immediately.