Put the carrots in a 10- to 12-inch saute pan (they should be almost in a single layer) and add enough water to come halfway up the sides of the carrots. Add the butter, maple syrup, and salt, 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), about 10 minutes. Uncover and continue to boil until the liquid evaporates and forms a syrup and the carrots start to caramelize and become lightly tinged with brown. Shake the pan and roll the pieces around to evenly glaze the carrots. Taste and add a pinch of salt, if needed, and serve.