In a medium bowl, mix together the self-rising flour and milk until dough is just starting to come together. Add the melted butter and mix until combined. May need to use hands to finishing mixing. Dough should be soft and smooth, like playdough.
In a small bowl, whisk together the filling ingredients - brown sugar, cinnamon, cornstarch, melted butter. Set aside.
Lightly flour or oil surface. Roll dough into rectangle shape, between 1/8- and 1/4-inch thick, about 12 inches by 8 inches. Spread filling over dough, leaving some space on the long edges. Roll dough up tightly, starting with long edge. Lightly pinch edge to seal. Cut into 9 rolls, each about 1 to 1 1/2 inches thick.
Oil your air fryer basket or use parchment paper. Lightly press down on the tops of each roll. Place rolls in the air fryer. Cook at 350˚F/177˚C for 5 minutes. (Cooking time may vary depending on your air fryer.)
Meanwhile, mix together cream cheese, powdered sugar, vanilla, and milk for the icing.
Pipe or spread the icing over the tops of the warm rolls. Best served warm and fresh. Enjoy!