Begin the day before you plan to bake. In a large bowl or electric stand mixer, combine the sourdough starter, water, sugar, melted butter and eggs. Mix until smooth, then add the flours and salt. Mix with a dough hook attachment for about 5 minutes (or knead by hand for 10 or more minutes), until the dough is smooth and elastic.
Cover the bowl loosely with a damp cotton towel or plastic wrap, and put it in a warm place to rise. After two hours, move the bowl to the refrigerator to continue slowly rising for 6-12 hours.
After this rise, shape the cinnamon rolls. Prepare a floured surface and lightly coat a 9x13 inch baking dish with butter. In a small bowl, mix the brown sugar, white sugar and cinnamon. Take the dough out of the refrigerator and roll out on the floured surface into a large rectangle about 12x18 inches. Spread softened butter evenly over the dough's surface, and sprinkle the cinnamon sugar mixture all over. Starting with a long side of the rectangle, tightly roll the dough into a log and pinch the seam closed. Slice the log into 12 equal buns using dental floss or a sharp knife. Arrange the 12 buns in the prepared baking dish, leaving space in between buns to allow room to rise. Cover the dish with plastic wrap and refrigerate overnight.
The next day, when you're ready to bake, preheat the oven to 375 F and transfer the rolls from the refrigerator to a warm place to proof for about 30 minutes, until lightly plumped. Remove the plastic wrap from the dish and bake for about 25 minutes, until puffy and golden.
While the rolls begin to cool, prepare a glaze. Mix together the powdered sugar, maple syrup, coffee and salt; then drizzle all over the rolls