Preheat oven to 350°F with rack in middle. Butter a 9-inch square baking pan.
Whisk together flour, ginger, baking soda, cinnamon, and salt in a bowl. Beat butter and sugar with an electric mixer at medium speed until pale and fluffy. Beat in egg until blended, then beat in molasses and buttermilk.
Mix in flour mixture on low speed until smooth, then add hot water and beat 1 minute (batter may look curdled.)
Spread batter evenly in pan and bake until a wooded pick inserted into center comes out clean, 40 to 45 minutes. Cool in pan on a rack.
Gingerbread can be made 1 day ahead and kept in pan at room temperature (covered once cool).