Preheat oven to 350°F (175°C). Grease and line a 9x9 inch pan.
Whisk flour, baking soda, and salt in a bowl; set aside.
Beat butter and brown sugar until fluffy, about 2 minutes. Add eggs one at a time, then stir in bananas and vanilla. Fold in sour cream.
Gently mix dry ingredients into wet until just combined. Spread batter into prepared pan.
For streusel, rub butter into oats, brown sugar, flour, and cinnamon until clumpy; sprinkle over batter.
Bake 28–32 minutes until a toothpick comes out with a few moist crumbs. Cool before cutting.