Combine carrots, ginger, thyme, chicken broth, butter, sugar, 1 teaspoon salt, and a few grinds black pepper in a 12-inch straight-sided sautée pan or Dutch oven and place over high heat.
When liquid boils, cover and cook, stirring occasionally, until carrots are almost completely tender, about 10 minutes.
If liquid drops to below ½-inch during cooking, top up with a cup of hot water.
Remove lid and continue cooking carrots at a rapid boil.
Combine cornstarch with 1 teaspoon water in a small bowl and stir with a fork until homogenous.
Pour cornstarch mixture into carrots and stir to combine.
Continue cooking until sauce is reduced to a syrupy glaze.
Pick out thyme sprigs and discard.
Off heat, add lemon juice and stir to combine.
Season to taste with more salt and pepper.
Transfer to a serving dish and serve.
