Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.
Place bananas into a large resealable plastic bag; seal the bag and smoosh bananas with your fingers until well mashed. Set aside.
Mix together brown sugar and butter in a large bowl with an electric mixer on medium speed until light and fluffy, 1 to 2 minutes. Cut a corner from the plastic bag; squeeze mashed bananas into brown sugar mixture in the bowl.
Add egg, milk, cinnamon, and vanilla extract; beat on medium speed until well combined.
Mix in flour, baking powder, baking soda, and kosher salt in a seperate bowl, then add into wet ingredients. Mix on low speed just until smooth, about 1 minute. Spread into the prepared loaf pan.
Bake in the preheated oven until lightly browned on top and a toothpick inserted into the center comes out clean, about 40 minutes.
