Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the sliced bananas and 1/2 cup of the sugar. Let them sit for about 10 minutes to release their juices.
In another bowl, whisk together the flour, remaining sugar, baking powder, salt, and cinnamon.
Add the milk, melted butter, and vanilla extract to the dry ingredients. Stir until just combined.
Pour the batter into a greased 9x13-inch baking dish. Evenly distribute the banana mixture over the batter. If using, sprinkle the chopped pecans on top.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Let the cobbler cool for about 10 minutes before serving. It can be enjoyed warm or at room temperature.