This moist, cakelike version of the perennial favorite is made with fresh ginger and unsulfured molasses.
Heat oven to 325 degrees. Butter an 8-inch square pan, and line with buttered parchment paper; set aside. Combine butter and brown sugar in the bowl of an electric mixer fitted with paddle attachment; mix on medium speed until creamy. Add molasses, egg, and salt; mix until smooth.
Combine flour and baking soda in a small bowl. Add half the flour mixture to butter mixture, and mix until combined. Add 1/4 cup buttermilk, and mix until combined. Repeat with remaining flour mixture and remaining buttermilk. Stir in ginger until thoroughly combined.
Pour batter into prepared pan, and bake until firm to the touch and golden brown, 40 to 45 minutes. Cool in pan on a wire rack for 10 minutes before unmolding.