8 tablespoons (1 stick) unsalted butter, at room temperature
1 cup sugar
2 large eggs, at room temperature
4 tablespoons (1/2 stick) unsalted butter, cut into pieces
1 1/2 cups confectioners' sugar
3 1/2 tablespoons heavy cream
1/4 teaspoon vanilla extract
1/4 teaspoon salt
How to Make It
Preheat oven to 350°F; butter and flour a 9-inch springform pan. In a bowl, whisk flour, baking powder, baking soda, salt and nutmeg. In a separate bowl whisk buttermilk, bananas and vanilla.
In a large bowl, using an electric mixer on medium-high speed, beat butter and sugar until light, about 3 minutes. Beat in eggs 1 at a time. Scrape down sides and bottom of bowl; beat again. Beat flour mixture into butter mixture in thirds, alternating with half of banana mixture, until batter is smooth. Spread batter in pan.
Bake cake until golden and a tester inserted into center comes out clean, about 45 minutes, rotating halfway through. (Tent pan with foil if cake is browning too quickly.) Cool completely in pan on a wire rack.
Make icing: In a skillet over medium heat, melt butter, swirling occasionally, until it has stopped foaming and milk solids in bottom of pan have turned golden brown and smell nutty, about 7 minutes. Transfer to a bowl and let cool slightly. Whisk in confectioners' sugar, cream, vanilla and salt until smooth.
Run a knife around inside edge of pan; release cake ring. Spread icing on top; serve.