Instructions

• Preheat oven to 350°F (175°C). Grease a 13×18-inch baking sheet pan.
• In a mixer or large bowl, beat together 1 cup sugar, 1 cup plain Greek yogurt, and 1/2 cup softened butter until light and fluffy.
• Add 2 large eggs, 2 cups mashed bananas (about 4 medium bananas), and 2 teaspoons vanilla. Mix until well combined and smooth.
• Add 2 cups flour, 1 teaspoon baking soda, and 1 teaspoon salt. Mix just until combined and no streaks of flour remain.
• Pour the batter into the prepared sheet pan and spread it evenly.
• Bake 25–30 minutes, until the top is golden brown and springs back when lightly pressed.
• Remove the cake from the oven and let it cool in the pan for about 10 minutes (the cake should be warm but not hot when you frost it).
• While the cake cools, brown 1/4 cup butter for the frosting: cut the 1/4 cup butter into pieces and cook in a small sauté pan over medium heat, stirring constantly for about 5–8 minutes, until it foams and turns golden brown. Remove from heat and pour the browned butter into a heatproof bowl to stop the cooking; let it cool until warm (not hot).
• Add 1 cup confectioners’ sugar, 2 tablespoons milk, and 1 teaspoon vanilla to the warm browned butter. Beat until the frosting is smooth and creamy.
• Pour the frosting over the warm (not hot) cake and spread to cover the surface evenly.
• Slice the cake into 24 even pieces. Serve warm or cool.