Pour water and starter into a bowl. Break the starter up until mixture is milky. Add in flour, sugar, and salt. Mix until no dry bits remain. Cover and let rest for 30 minutes.
Dough Development
After 30 minutes, perform a set of stretch and folds. Cover, and repeat 3 more times, with a 30 minute rest between.
Bulk Rise
Cover dough and let rise overnight, or 8-12 hours. Dough should about double. More or less is okay.
Second Rise
Pour a few tablespoons of oil into a 9x13 pan and spread around. I like to also use parchment paper to ensure no sticking.Pour the dough unto the pan, folding the edges up slightly on itself so that the bottom and edges are well coated in oil.Gently stretch the dough to fill the pan the best you can. It is okay if it doesn't quite fill the pan, it will relax and spread during the final rise.Cover and let rise for about 2 hours. The dough should be very puffy and about doubled.
Dimple and Top Dough
Preheat oven to 450° and move a rack to the lower part of the oven.
Pour a small amount of oil on the top of the puffed up dough and very gently spread it around.Use your fingers to dimple the dough, pushing them all the way to the bottom of the pan to create craters for the sugar to collect into!
Mix the brown sugar and cinnamon together. Sprinkle over the top of the dough. Drizzle the melted butter over top of this.
Bake
Bake for 20-25 minutes on the lower rack of the oven until the dough is browned.
Let rest in pan for 5-10 minutes before removing from the pan to a cooling rack to keep it from softening on the bottom.
Icing
Whip together softened butter and cream cheese until fluffy, about 2-3 minutes. Add in sugar 1/2 cup at a time, whipping thoroughly after each addition. Finally, add in the vanilla and whip for an additional minute.
Notes
*This amount of sugar is required for "non-hazardous" cream cheese icing that doesn't require refrigeration. Feel free to reduce to your taste.