Preheat oven to 350°F. Grease two 8x4 inch loaf pans or line with parchment paper.
In a small bowl, mash the bananas with brown sugar, vanilla extract, and ¾ tsp cinnamon until mostly smooth (a few small chunks are fine). Set aside.
In a large bowl, beat softened butter and white sugar with an electric mixer for about 3 minutes until pale and fluffy.
Add eggs one at a time, beating well after each addition.
Sift together 2 cups flour, baking soda, and salt. Add to butter mixture gradually, stirring just until combined (flour streaks are okay).
Fold in sour cream until smooth, then fold in the mashed banana mixture until no banana streaks remain. Don't overmix.
For the crumb topping: Mix 1 cup flour, 1 cup brown sugar, and 1 tsp cinnamon in a bowl. Cut cold butter into small cubes and add to the mixture.
Use a pastry cutter or two forks to cut the butter into the flour mixture until it resembles coarse breadcrumbs with pea-sized butter pieces.
Divide batter evenly between the two prepared loaf pans. Sprinkle all of the crumb topping over both loaves, pressing gently to help it adhere.
Bake for 35-40 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs. If the top browns too quickly, tent with foil.
Let loaves cool in pans for 10 minutes, then transfer to a wire rack to cool completely before slicing with a serrated knife.