Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and set aside.
In a medium bowl, whisk together 1 1/2 cups flour, baking soda, salt, and 1/2 teaspoon cinnamon. Set aside.
In a large bowl, cream together 1/2 cup softened butter and granulated sugar until light and fluffy, about 3 minutes.
Add eggs one at a time, beating well after each addition. Stir in vanilla extract.
Mix in the mashed bananas, sour cream, and milk until combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
In a small bowl, combine brown sugar, 1/2 cup flour, and 1 teaspoon cinnamon for the topping.
Cut in the cold butter pieces with a pastry cutter or fork until the mixture resembles coarse crumbs.
Pour the banana bread batter into the prepared loaf pan and evenly sprinkle the crumb topping over the batter.
Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.