Heat oven to 375°F. Using 1 tablespoon of the butter, generously butter 12-cup fluted tube cake pan. In small microwavable bowl, microwave remaining butter on High 1 min or until melted when stirred.
Separate both cans of dough into 16 rolls. Cut each roll in half crosswise; place half of roll pieces in pan. Sprinkle with half of the dry pudding mix and half of the brown sugar. Drizzle with half of the melted butter. Repeat with remaining roll pieces, pudding mix, brown sugar and melted butter. Sprinkle with chocolate chips.
Bake 24 to 28 minutes or until rolls are deep golden brown and dough appears done when slightly pulled apart. Cool in pan 2 minutes. Place heatproof serving platter upside down over pan; turn platter and pan over. Remove pan. Cool 15 minutes.
Remove lid from icing. Microwave icing on High 10 to 15 seconds or until of drizzling consistency. Drizzle icing over ring. Cut into wedges to serve.