For the carrots: Place the carrots in a 10-inch saute pan. Add 1 1/2 cups water, the sugar or maple syrup and salt. Place the pan over high heat and bring to a boil, stirring occasionally with a rubber spatula to dissolve the sugar. Reduce the heat to medium-high and continue to simmer vigorously, stirring occasionally, until the liquid has thickened to a syrup and the carrots are fork tender, about 12 minutes. Stir in the butter. Remove from the heat and cool for 5 minutes before serving.
For the gremolata: Meanwhile, mix together the walnuts, parsley, thyme, lemon zest and salt in a medium bowl.
To serve, gently toss the carrots to coat them in the thickened syrup. Spoon them onto a platter and sprinkle with half of the gremolata. Serve the remaining gremolata on the side.