Mix flour, brown sugar, baking powder, and salt together in a large bowl.
Mash bananas in a large bowl using a fork. Add milk, egg, oil, and vanilla extract; mix well.
Stir banana mixture and chocolate chips into the flour mixture until batter is blended but still slightly lumpy.
Heat a lightly oiled griddle over medium heat. Drop 1/4 cup batter onto the griddle and cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.