In the bowl of a stand mixer, combine bread flour, potato flake sourdough starter, melted butter, salt, sugar, and warm water.
Using the dough hook, mix until the dough comes together and becomes smooth and elastic.
Cover the dough and allow it to rise until doubled. This will take about 6-10 hours. Don't let it rise more than double.
After the first rise, shape the dough into a loaf.
Cut five deep slits across the top of the dough, being careful not to cut all the way through. Make sure you use a really sharpe knife or scoring blade.
In a shallow dish, mix together white sugar, brown sugar, and cinnamon.
In a separate dish, melt the butter. Add corn syrup. Stir until combined.
Dip the shaped dough into the melted butter mixture. Use your fingers to gently open the slits and work the butter down into the cuts.
Transfer the dough into the cinnamon sugar mixture and coat as much of the dough as possible. Opening the slits to coat inside with the cinnamon sugar mixture.
Place the coated dough into a parchment-lined loaf pan.
Sprinkle about half of the remaining cinnamon sugar mixture down into the slits. Reserve the remaining butter and cinnamon sugar mixture for after the second rise.
Cover the pan with plastic wrap and allow the dough to rise until doubled and puffy.
Before baking, pour the remaining butter mixture over the top of the dough.
Sprinkle the rest of the cinnamon sugar mixture over the top.
Bake at 350°F for 25 minutes.
Loosely cover with foil and bake for about 6 more minutes, or until the bread is baked through (200℉ internal temperature.)
While the bread bakes, mix together powdered sugar, vanilla, and whole milk until smooth.
Allow the bread to cool slightly, then drizzle about half of the icing over the top.
Serve the remaining icing on the side for dipping, if desired.