The darker the brown sugar, the deeper the cookies' flavor. You could use a more exotic brown sugar in this recipe, such as Billington's dark brown cane sugar from England or light or dark muscovado sugar.
Line two baking sheets with parchment. Combine the butter, brown sugar, and salt in a stand mixer bowl (use the paddle attachment) or a large mixing bowl. Mix on low speed until the butter combines with the sugar but isn't perfectly smooth, 1 to 2 min. Add the flour and oats and mix on low speed, scraping the bowl frequently, until the dough has just about pulled together, about 3 min.; don't overmix.
Roll: On a lightly floured surface, roll the dough to about 1/4 inch thick. Aim for a uniform thickness to ensure even baking.
Cut: Cut the dough into bars or squares with a sharp knife or, using cookie cutters, cut out shapes as close to one another as possible. Press the scraps together, roll them out, and cut out more cookies. If the dough becomes sticky, refrigerate it briefly. Arrange the cookies on two parchment-lined baking sheets and refrigerate until chilled, at least 20 min.
Bake: Position oven racks in the upper and lower thirds of the oven and heat the oven to 300°F. Bake the cookies until golden on the bottom and edges and pale to golden on top, 30 min. to 1 hour. (After 15 min., swap the position of the baking sheets and rotate them 180 degrees for even baking.) If the cookies are done before 30 min., reduce the oven temperature to 275°F for the remaining batches; if they take longer than 1 hour, increase the temperature to 325°F.
Photo: Scott Phillips