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, and salt. Set aside.
In a large bowl, beat the softened butter, granulated sugar, and 1/4 cup brown sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Mix in the mashed bananas and buttermilk until combined.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Prepare the brown sugar streusel by combining 1/3 cup brown sugar, 1/4 cup flour, and ground cinnamon in a small bowl.
Cut in the cold cubed butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Pour the banana bread batter into the prepared loaf pan and spread evenly.
Sprinkle the brown sugar streusel evenly over the top of the batter.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the bread cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.