To make the dough: Mix all the ingredients except the butter in a kitchen aid stand mixer with paddle attachment until the flour is evenly moistened and the dough has formed a cohesive, sticky mass, 2 to 3 minutes on low speed of a stand mixer.
Gradually add butter and incorporate about 1 minute on low speed. Once all the butter is incorporated, turn the mixer up one speed and knead the dough until it’s smooth and supple though still somewhat soft and tacky, about 2 to 3 minutes.
Cover the dough and let it rest in a warm (75°F) place for 8 to 12 hours. To develop strength in the dough, stretch and fold it in the bowl three to four times during the rest. This will increase the elasticity of the dough.
To make the filling:
In a medium bowl combine brown sugar, all-purpose flour, melted butter, cinnamon and salt . The texture of the mixture will be somewhat like wet sand.
Turn the dough out onto a lightly greased or floured work surface and gently deflate it, patting or rolling it into a 14” x 20” rectangle.
Spread the filling evenly over the surface of the dough, leaving 1/2” of exposed dough along one short edge.
Starting with the filling-coated short edge, roll the dough into a log. As you roll, the log will lengthen to around 18".
Cut the log into twelve 2” slices and place them in a lightly greased 8-inch cast iron skillet. Cover the pan and let the buns rise until they’re puffy, 2 to 3 hours.
If you want, you can store the buns in refrigerator for overnight or up to 24 hours and bake next day.
To bake the same day: Bake the buns in a preheated 400°F oven for 22 minutes, until golden. A digital thermometer inserted into the center of a middle bun should read 190°F.
To make the icing: While the buns are baking, stir together all the ingredients in a medium bowl until smooth.
Remove the buns from the oven and cool for 5 to 10 minutes before icing. Alternatively, allow the buns to cool to room temperature