Preheat oven to 350°. In a large bowl, 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.
Transfer to a greased 10-in. cast-iron or other ovenproof skillet; sprinkle with remaining 1/2 cup chocolate chips. Bake until a toothpick inserted in center comes out clean, 25-30 minutes. Cool in pan on a wire rack.