Preheat oven to 350°F. Spray a 9” square pan or a 10” pie plate with cooking spray.
Add 1/2 cup (8 tablespoons) of unsalted butter to a small frying pan. Cook over low heat, stirring until it browns. It will foam up, then turn brown. Keep stirring the entire time. Once it turns brown the foam will diminish and the butter will become golden. Remove from heat. You are using this butter for both the cake and streusel.
Mix sugar, 1/4 cup of the browned butter, and egg in a large bowl. Stir in baking powder and salt, then stir in mashed bananas. Whisk in flour and milk stir until just combined. Pour in prepared pan.
Make the crumb topping: stir together brown sugar, flour, cinnamon, and remaining 1/4 cup browned butter, and nuts, if using. I like to stir them together with a fork.
Top cake with the streusel. Bake time will depend on pan, but it will take anywhere from 30-40 minutes. My thin pie plates and 9-inch pans take about 30 minutes, but the thick pan used in the photos took 40.
Cool slightly before serving.