Cut the carrots in half lengthwise. Holding your knife at a sharp angle, cut each half into 1/4-inch-thick slices to make half-moons. Put the carrots and shallots in a 10- to 12-inch sauté pan and add enough broth to come halfway up the sides of the vegetables. Add-the butter, salt, and sugar and bring to a boil over high heat. Cover the pan with the lid slightly askew, reduce the heat to medium high, and cook at a steady boil, shaking the pan occasionally, until the carrots are tender but not soft (a paring knife should enter a carrot with just a little resistance), 8 to 10 min. Uncover, add the thyme, and continue to boil until the liquid evaporates. Continue to cook the carrots and shallots over medium-high heat, stirring occasionally, until they begin to caramelize and turn golden brown, 3 to 4 min. Taste and add a pinch more salt, if necessary, and serve.
Photo: Sarah Jay