Brown Sugar Banana Snack Cake with Vanilla Frosting

for the cake:

1 cup packed dark brown sugar

¼ cup unsalted butter

2 large eggs

1 cup light sour cream

1 ½ cups mashed very ripe bananas (from about 3 large bananas)

2 teaspoons pure vanilla extract

2 cups all-purpose flour

1 teaspoon baking soda

½ teaspoon salt

for the vanilla frosting:

¼ cup unsalted butter, softened

2 ½ cups powdered sugar

1 tablespoon pure vanilla extract

¼ cup + 3 tablespoons heavy cream