Preheat oven to 325°. In the bowl of your mixer, beat butter and sugar until crumbly. Beat in egg, bananas and vanilla.
In another bowl, whisk flour, baking soda and salt; gradually beat into banana mixture. Stir in 1/2 cup chocolate chips.
Pour into a greased 10-in. cast-iron or other ovenproof skillet; sprinkle with remaining 1/2 cup chocolate chips. Bake approximately 30 minutes at 350°. Reduce oven temp to 300° and bake another 15-20 minutes, until a toothpick inserted in center comes out clean. Cool in pan on a wire rack.