Place water in a large 5- or 6-qt. pot. Add salt and stir. Bring water to a boil and add the barley, stirring. Turn the heat to medium so it is still boiling, but not fiercely. Cook for 45 minutes.
While the barley is cooking, put the butter in a small saucepan. Turn the heat to medium-high and stir the butter as it melts. When it has melted, tilt and tip the pan so the melted butter moves all around the bottom and doesn't burn. When the butter turns a rich caramel color, remove from the heat. It should be brown, but not dark brown. This takes only a couple of minutes so don't turn your back on it. Set aside.
Place the scallions on a cutting board and trim off the root ends and 4 or 5 inches of the coarse green tops. Finely chop the onions. Set aside.
When the barley has cooked for 45 minutes, check it for doneness by scooping out a few grains and tasting them. If chewy and tender, the barley is done. If grains are still tough and firm, cook the barley for 15 minutes longer. When done, pour the water and barley into a strainer.
Measure 3 cups of cooked barley and put into a serving bowl. (Let the remaining barley cool, then transfer to a container, cover tightly and refrigerate or freeze until needed.)
Add the brown butter and scallions to the barley in the bowl, taste and add more salt and some pepper if needed. Serve hot.