Melt 1/3 cup unsalted butter in saucepan. Let cool.
Mix warm milk and yeast together. Stir together and wait for it to bloom.
In a large bowl, combine 1/2 cup granulated sugar, 1 tsp salt, cooled melted butter, and yeast mixture. Add eggs one at a time.
Add 3.5 cups flour slowly. Once you are able to touch the dough without it sticking too much to your hands, you are good.
Use remaining 1/2 cup flour to flour your surface. Knead dough for 6-8 minutes until smooth ball.
Grease a large bowl with oil. Oil your dough ball. let rise in warm place until doubles in size; 1-2 hours.
Once doubled in size, punch down dough to redistribute growth. Roll out dough to a 15x10 rectangle. Spread brown sugar mixture filling over dough. Roll dough lengthwise. Cut into 12 rolls.
Grease 12 inch cast iron skillet. Put rolls on skillet. Cover, let rise another 45 minutes.
Mix together 1/4 cup rum chata and 1/4 cup heavy cream. Set aside until ready to bake.
Once risen for a 2nd time, add rum chata cream mixture. Bake at 375 for 22-24 minutes. Once slightly cooled, put frosting on top.