In a large bowl, mash bananas with dark brown sugar, egg, and vanilla extract until mostly smooth; set aside.

In a small saucepan or skillet, melt butter over medium heat. Cook, stirring often, until butter solids turn golden brown and smell nutty, 4 to 6 minutes. Remove saucepan from heat and whisk in cinnamon. Let cool slightly, about 5 minutes.

In a medium bowl, whisk together all-purpose flour, baking powder, baking soda, and salt; set aside.

Pour butter over banana mixture and whisk to combine. Add buttermilk and whisk to incorporate. Add flour mixture, whisking until just combined. Using a flexible spatula, fold in walnuts, if using.

Place a wire rack inside a rimmed baking sheet; set aside.

Heat a large electric nonstick griddle to medium heat (350°F/175°C) or large nonstick, cast iron, or carbon steel skillet or stovetop griddle over medium heat. Melt ½ tablespoon butter and, using a ⅓ cup scoop or measuring cup, scoop batter onto griddle or skillet to form 3-inch pancakes spaced ½- to 1-inch apart, working in batches if necessary. Cook until bubbles start to appear on top of batter and bottoms are golden brown, 2 to 4 minutes, adjusting heat as needed to prevent overbrowning. Carefully flip pancakes and cook until bottoms are lightly golden and pancakes are cooked through, 2 to 4 minutes. Transfer to prepared wire rack. Repeat with remaining batter. Serve warm with maple syrup.