Beat together butter and brown sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer or 5 minutes with a handheld, then add egg, beating until combined well. Reduce speed to low and alternately mix in flour mixture and buttermilk in batches, beginning and ending with flour, scraping down sides of bowl occasionally, and mixing until smooth.

Spoon ¼-cup mounds of batter about 2 inches apart onto 2 buttered large baking sheets. Bake in upper and lower thirds of oven, switching position of sheets halfway through baking time, until tops are puffed and cakes spring back when touched, 11 to 13 minutes. Transfer with a metal spatula to a rack to cool completely.