Peel the carrots and trim off the ends. Cut the carrots on the diagonal into reasonably thin slices (around ¼in, ½cm thick).
Melt the butter over a medium heat in a medium skillet/frying pan large enough to hold all the carrots, but without too much extra space. Once the butter has melted, add the sugar, stir to dissolve, then add the carrots.
Toss the carrots gently in the butter to coat then add the water. You want to add enough to just about cover the carrot slices, but it's fine to have the tops sticking out a little.
Bring the liquid to a boil and reduce the heat so that it simmers. Continue to cook for around 20 minutes until the liquid evaporates and the carrots are tender to a knifepoint. If they are not as fresh or slices are thicker, you may want to cook some of the time at the start with a lid on to help them steam and cook more, but I don't generally find I need to. Stir the carrots a couple of times as they cook to turn the slices and ensure those at the top swap to the bottom so all spend part of the time in the liquid.
Once the liquid has evaporated, apart from a slight buttery glaze, and the carrots are tender, add a little salt and pepper, to taste, the parsley and lemon juice. Stir to coat evenly then serve.
Video
Notes
Note video and photos show a half quantity but the process is exactly the same.