In the pan of your bread machine or kitchen aid, combine water, melted butter, vanilla pudding mix, warm milk, egg, white sugar, salt, flour and yeast. Set machine to Dough cycle; press Start and let beat for 10 minutes then stop it. Or beat ingredients in kitchen aid for 10 minutes. Let dough rest in bread machine / kitchen aid for 10 minutes.
When Dough cycle has finished, turn dough out onto a lightly floured surface and roll out into a large rectangle shape until dough is 1/2 inch thick, if recipe is scaled larger, you might need to make additional rectangles as you don’t want to make them into a long log that you cannot roll with two hands. Spread rectangle with softened butter. Sprinkle brown and cinnamon over dough, you don’t have to stick exact with the measurements, they are just guidelines for buying and portioning out the filling.
Roll up dough, beginning with long side. Slice into 16 (or more) one inch slices and place in 9X13 inch buttered pan (you can also use muffin tins! Also 9X13 inch pan refers to original serving amount not scaled amount). Let rise in a warm place until doubled, about 30 - 45 minutes. Meanwhile, preheat oven to 350 degrees F (175 degrees C).
Bake in preheated oven for 15 to 20 minutes. While rolls are baking, stir together the cream cheese, softened butter, confectioners' sugar, vanilla and milk. Remove rolls from oven, let cool, and top with cream cheese frosting.