Follow the manufacturer's recommendations to add all ingredients into the bread machine pan. Start the Dough cycle.
When dough doubles in volume, transfer it to a work surface dusted with flour. Let rest. Meanwhile, mix brown sugar with cinnamon in a small bowl.
Roll dough out to 16 by 21 inches big. Top the dough rectangle with 1/3 cup butter, spread evenly. Sprinkle with cinnamon sugar and roll up. Cut the big roll into 12 small buns. Arrange them in a 9x13-in baking pan. Cover and let rise till doubled. While waiting, preheat oven to 400°F/200°C/Gas Mark 6.
Bake for 15 minutes. Meanwhile, beat cream cheese with ¼ cup butter, vanilla, confectioner’s sugar and salt. Remove buns from the oven, let cool till warm; top with frosting and serve.