Step 1: In a large bowl, whisk together the warm milk, sugar, and yeast. Let it sit for 5 minutes until foamy.
Step 2: Add the sourdough discard, softened butter, and egg to the yeast mixture. Stir until well combined.
Step 3: Gradually add the flour and salt, kneading by hand or with a stand mixer for about 5-7 minutes until a smooth, slightly tacky dough forms.
Step 4: Place the dough in a greased bowl, cover, and let rise in a warm spot for 1-1.5 hours or until doubled in size.
Step 5: Roll the dough out on a floured surface into a 12x18 inch rectangle. Spread with softened butter and sprinkle with the cinnamon-sugar mixture.
Step 6: Roll the dough tightly into a log and cut into 12 even pieces using unflavored dental floss or a sharp knife.
Step 7: Place the rolls in a greased 9x13 baking dish. Cover and let rise for another 45 minutes.
Step 8: Bake at 350°F (175°C) for 22-25 minutes until golden brown.
Step 9: While rolls are cooling slightly, whisk together the frosting ingredients and spread generously over the warm rolls.