Preheat oven to 375. Prepare a 9x13 pan by spraying it with non stick cooking spray.
In a large bowl, beat together sugar, yogurt, butter and eggs until smooth. Add in mashed bananas and vanilla and continue to blend. In a smaller bowl combine flour, baking soda and salt. Stir dry ingredients into the wet ingredients. Finally stir in chocolate chips.
Spread batter into pan and bake 25-35 minutes, or until a toothpick comes out clean when poked into center.
Allow to cool in pan. Once cake is cooled completely, frost with browned butter chocolate frosting.