In a bowl of a stand mixer with a dough hook attachment, combine fed sourdough starter, flour, sugar, warm water, salt, and melted coconut oil. Mix together until it forms into a ball and the dough is pulling away from the sides.
Remove the dough and form into a ball and place in a large greased bowl. Cover tightly with plastic wrap to prevent the dough from drying out and let it set in a warm place throughout the day (or about 8-12 hours).
That night, or 8-12 hours later, after the dough has about doubled, remove the dough onto a lightly floured surface. Press the dough flat into a rectangle. Then, using your rolling pin, roll out the dough into a large rectangular shape about 1/4 of an inch thick.
Melt the butter and baste onto the dough, covering the entire surface, all the way to the edges. Sprinkle the sugar and cinnamon on top.
Leave about 1 teaspoon of butter in the container you melted it in. Using your basting brush, apply the rest of the butter to the baking dish that you plan to bake your cinnamon rolls in.
Roll the dough up as tightly as you can. Starting at the top and working your way down. When you get to the end, pull it up tightly and pinch the ends into the main roll.
The best to way keep the circular shape of your cinnamon rolls is to cut them using thread or unflavored floss.
Once in the dish, allow for the cinnamon rolls to rise for a second time about 8-10 hours, or until doubled, depending on temperature.
After the cinnamon rolls have risen, pour about 1/2 cup of milk into the dish allowing it to surround the cinnamon rolls. This is step is optional but makes a much more gooey and moist cinnamon roll.
Bake the cinnamon rolls in a 350 degree oven for about 25-30 minutes, or until the tops are golden brown. While they are baking prepare the icing. When the cinnamon rolls are done, allow them to cool slightly and top them with icing.
Mix powdered sugar, milk, butter, and maple extract together. Whisk until smooth. Pour and spread over your freshly baked cinnamon rolls and enjoy!