Cut the carrots evenly: Peel the carrots and slice them into 1/2-inch coins. Slice the thick top end on a diagonal or halve it lengthwise first so every piece is about the same size.
Steam them covered: Put the carrots, water, and 1/2 teaspoon salt in a large skillet. Cover, set it over medium heat, and cook for 8-10 minutes, until a paring knife slides into a coin with just a little resistance left.
Boil off the water: Take the lid off and turn the heat up to medium-high. Let the remaining water cook away, about 1-2 minutes. The pan should look nearly dry before anything else goes in.
Build the glaze: Add the butter and brown sugar. Cook uncovered for 4-5 minutes, tossing the carrots often, until the sugar melts into a syrup that clings to the carrots and coats the back of a spoon.
Season and serve: Stir in the black pepper, taste, and add a pinch more salt if it needs it. Scatter the parsley over the top and serve warm.
Notes
Steam the carrots covered first, then let the pan cook nearly dry before the butter and brown sugar go in. Adding sugar to a wet pan gives you a thin syrup instead of a glaze. The carrots are ready when a paring knife slides in with slight resistance, about 8-10 minutes covered.