Preheat oven to 350°F. Butter a 9- by 2-inch round cake pan and dust with flour, knocking out excess.
Whisk together flour, cocoa, baking soda, and salt.
Beat together butter and brown sugar with an electric mixer until pale and fluffy. Add eggs 1 at a time, beating well after each addition, then beat in vanilla.
Add flour mixture and water alternately in batches, beginning and ending with flour and mixing just until combined.
Pour batter into cake pan and bake in middle of oven until springy to the touch and a tester inserted in center comes out clean, 55 minutes to 1 hour. Cool in pan 1 hour. Invert onto a rack, then turn right side up and dust with confectioners sugar. Enjoy!