Preheat oven to 350°F (175°C). Grease a 10-inch cast-iron skillet with butter or nonstick spray.
In a large bowl, mash the bananas until smooth. Whisk in the melted butter, sugar, egg, and vanilla until well combined.
Add the flour, baking soda, and salt to the wet ingredients. Stir with a spatula until just combined—don't overmix. Fold in 3/4 cup of the chocolate chips.
Pour the batter into the prepared skillet and spread evenly. Sprinkle the remaining 1/4 cup chocolate chips over the top.
Bake for 30-35 minutes, until a toothpick inserted into the center comes out clean or with a few moist crumbs. The top should be golden brown.
Let cool in the skillet for 15 minutes before slicing. Serve warm or at room temperature.