In a large bowl, mix together the sugar, egg, milk, salt, and sourdough starter until well combined. Gradually add the flour and stir until a rough dough forms. Using a stand mixer, or by hand, knead the dough until it begins to smooth out, then add the softened butter and continue kneading until the dough is soft, smooth, and elastic Cover and let the dough rise overnight in a cool place (70-75°F) for 8-10 hours.
Transfer the dough to a floured work surface. Using your hands, flatten the dough into a rough rectangle and then, using a rolling pin, roll out the dough into a rectangle about 6x12” with a thickness of around 1/2cm.
Combine brown sugar, cinnamon and corn starch in a bowl. Using your fingers or a pastry brush, brush the dough with softened, room temperature butter. Evenly spread the cinnamon-sugar mixture on top and using your hands, lightly press it into the dough.
Roll the dough tightly from the short end, like a scroll. Slice the log into three equal pieces using a sharp knife or string, and arrange the rolls on a parchment-lined baking dish. Cover the dish and let the rolls rise for 3–4 hours in a warm spot, such as an oven with the light on.
Preheat your oven to 375°F. Right before baking, pour heavy cream over the top of the cinnamon rolls to help them bake up softer and fluffier. Bake the cinnamon rolls for 20 minutes, or until the rolls starts to turn golden brown. Remove from the oven and let cool for about 20 minutes before serving.
Combine the glaze ingredients and stir until smooth. Drizzle the glaze over the warm cinnamon rolls, starting from the center to evenly coat them. Alternatively, dust with powdered sugar for a simpler finish. Serve and enjoy!