Cut a 12 inch circle from the parchment paper. Cut a small circle in the center Choose carrots that measure 3/4 to 1 1/4 in across the thickest end.
Bring water, butter and salt to a simmer in a 12-inch skillet over high heat.
Remove from heat, add carrots in a single layer, and place parchment round on top of the carrots. Cover skillet with lid and let stand for 20 minutes.
Remove lid from skillet, leaving the parchment round in place, and bring to a simmer over high heat.
Reduce heat to medium-low and simmer until almost all water has evaporated and carrots are very tender, about 45 minutes. Discard parchment round.
Increase heat to medium-high, and continue to cook caarrots, shaking pan frequently, until they are lightly glazed and no water remains in skillet, 2 to 4 minutes longer. Transfer to platter and serve.