Rinse the carrots well under cool water to remove any dirt. Peel off the outer skin with a vegetable peeler. Trim the tops and tips so each carrot looks clean and neat.
Cut the peeled carrots into pieces about ½ inch thick, slicing at an angle. Diagonal cuts give you more surface area, which means more glaze in every bite. Try to keep the pieces the same size so they cook evenly.
Place the sliced carrots in a large skillet and pour in the ½ cup of water. Cover the pan and cook over medium heat for about 7 minutes. The carrots should start to soften but still hold their shape.
Remove the lid and add the butter, brown sugar, maple syrup, salt, and cinnamon. Stir gently until the butter melts and the sugar dissolves. The liquid will begin to look syrupy and golden right away.
Keep cooking uncovered for another 7 to 8 minutes, stirring now and then. The glaze will thicken and coat the carrots in a shiny layer. Stop when the carrots are as tender as you like them.
Take the skillet off the heat and spoon the carrots onto a serving dish. Pour any extra glaze from the pan over the top. Serve right away while the glaze is still warm and sticky.