Preheat your oven to 375 degrees F and prepare a 9×13 inch pan by greasing it with non-stick cooking spray. This ensures your brownies will come out easily once baked.
In a large mixing bowl, cream together the granulated sugar and butter until the mixture is light and fluffy. This step is crucial, as it introduces air into the batter, which helps create a tender texture.
Add in the Greek yogurt and eggs, followed by the mashed bananas and vanilla extract. Mix thoroughly until well combined, allowing all those delicious flavors to meld.
In another bowl, combine the all-purpose flour, baking soda, and salt. Gradually add this mixture to the banana mixture, mixing just until moistened. Be careful not to overmix, or your brownies might become tough.
If desired, fold in any additional ingredients like nuts or chocolate chips at this point for added texture and flavor.
Spread the batter evenly into the prepared pan, smoothing out the top with a spatula. This will ensure even baking.
Bake in the preheated oven for 23 to 28 minutes. You’ll know they’re done when a toothpick inserted into the center comes out clean or with a few crumbs. Keep an eye on them to prevent overbaking.
While the brownies are baking, prepare the frosting. In a skillet over medium heat, melt the butter until it starts to turn a delicate brown, giving it a nutty aroma. Be cautious and stir constantly to avoid burning.
Remove the skillet from heat and whisk in the powdered sugar, vanilla extract, and 1 tablespoon of milk until the mixture is smooth. If it’s too thick, add more milk gradually.
Once the brownies have finished baking, pour the warm frosting over them while they are still warm, spreading it gently with the back of a spoon. Allow the brownies to cool completely before cutting them into squares.