In a large bowl, whisk together the sugar, egg, warm milk, salt, and sourdough starter until smooth. Gradually add the flour and mix until a shaggy dough forms.
Knead the dough using a stand mixer fitted with a dough hook or by hand until it comes together. Add the softened butter and continue kneading until the dough is soft, smooth, and elastic, about 8–10 minutes.
Cover the dough and let it rise on the counter for 8–10 hours, or until doubled in size.
Transfer the dough to a lightly floured surface. Gently press it into a rough rectangle, then roll it out to about 8 × 24 inches, roughly ½ cm thick.
In a small bowl, combine the brown sugar, cinnamon, and cornstarch. Crush or knife cut the walnuts into small pieces. Brush the surface of the dough evenly with softened butter. Sprinkle the cinnamon-sugar mixture over the dough followed by the crushed walnuts and gently press it in with your hands. Starting from the short side, roll the dough tightly into a log. Slice into six equal rolls using a sharp knife, thin kitchen twine, or dental floss.
Arrange the rolls in a prepared baking dish. Cover and let rise for 3–4 hours in a warm spot, such as an oven with the light on, until puffy.
Preheat the oven to 375°F (190°C). Just before baking, pour the heavy cream evenly over the rolls for extra softness. Bake for 20 minutes, or until the tops are lightly golden.
Remove from the oven and let the rolls cool for about 20 minutes.
Dust with powdered sugar or spread with your favorite cream cheese frosting, or enjoy as is!
Enjoy within three days. To reheat-- simply cover with a damp paper towel and microwave for 30 seconds.