Cut the carrots using the roll cut: Trim the tip of the carrot with a sharp diagonal cut. Roll the carrot 180 degrees and cut off a 1-inch piece, keeping your knife at the same diagonal angle as the original cut. Continue to roll and cut the carrot in this way. If the carrot widens dramatically toward the top, adjust the knife angle and carrot length so the pieces are all about the same size.

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.