Cut the butter and flour for dough together. Add buttermilk, starter, and honey; mix until dough is tight. Cover and let rest for 8 hours, or overnight.
Preheat the oven to 375 degrees F (190 degrees C). Butter 2 round baking pans.
Add baking powder, salt, and baking soda to the dough. Use your hands to incorporate.
Generously flour a countertop so that the dough doesn't stick; generously flour the top of the dough for the same reason. Roll the dough into a 20x12-inch rectangle.
Mix brown sugar and cinnamon together. Spread 2 tablespoons melted butter over the dough, avoiding the edges. Spread the cinnamon-sugar mixture over the melted butter. Roll the dough into a log, starting from the bottom. Use a bench scraper or sharp knife to cut the log into 1 1/2-inch segments. Arrange in the prepared baking pans, leaving a little space between each one.
Bake in the preheated oven until golden, 35 to 40 minutes.
While cinnamon rolls bake, mix confectioners' sugar, butter, milk, and vanilla extract for icing together in a bowl. Top the rolls with your icing right when they come out of the oven.