Preheat oven to 350°. Butter and flour a 9-in. square pan.
Make cake: Beat butter, brown sugar, and zest in a large bowl with a mixer until fluffy. Add eggs and beat until well blended. In another bowl, combine flour and other dry ingredients. Add flour mixture to butter mixture one-third at a time, alternating with buttermilk half at a time, and beating on low speed after each addition until blended. Spread batter in pan.
Bake until a toothpick inserted in center comes out clean, 25 to 30 minutes. Let cool on a rack, 10 minutes. Loosen cake from pan with a slender spatula, then invert onto a rack. Re-invert onto another rack; cool completely.
Make frosting: Cook butter in a medium saucepan over medium-low heat, swirling pan occasionally, until deep golden brown, 10 to 15 minutes. Pour into a mixer bowl, let cool, then chill until firm enough to beat, about 30 minutes. Add remaining ingredients except for nuts and beat until fluffy, 1 to 2 minutes, occasionally scraping inside of bowl.
Split cake horizontally with a long serrated knife. Lift off top layer with 2 wide spatulas. Set bottom layer on a platter, then spread with half of frosting. Replace top layer. Spread top of cake with remaining frosting, then sprinkle with nuts.