Add the warmed milk to the bowl of a stand mixer fitted with a dough hook*. Sprinkle with yeast and let sit for 5 minutes, or until foamy. If the yeast does not foam, it is dead and you'll need to start over with fresh yeast.
Add granulated sugar, beaten egg, sourdough discard, flour, and salt. Mix on low until combined, adding the melted butter as it mixes. Transfer the dough to a work surface and knead for 3-4 minutes until a soft, smooth dough forms (the dough should not be sticky). If needed, add more flour or milk (1 Tablespoon at a time) to reach your desired consistency.
Transfer the dough to a large, greased bowl. Cover with plastic wrap and let rise for 60-90 minutes, or until doubled in size. While the dough rises, soak the raisins in a bowl of hot water (this helps the raisins plump up if they've been sitting in your pantry for a while!).
Transfer the dough to a floured work surface. Use a rolling pin to roll the dough into a 12x18-inch rectangle**. Drain the raisins. Spread the dough with softened butter and evenly sprinkle with brown sugar, cinnamon, and raisins (optional).
From the long end of the rectangle, roll the dough into a log, pressing the seam along the edge of the dough to close. Use unflavored dental floss or a sharp knife to cut the log into 12 approximately equal-sized pieces. If using dental floss, wrap the floss around the log, then cross the ends over each other and pinch to cut.
Transfer the cut rolls to a greased 9x13-inch baking pan, face up. The rolls may not be touching, and there should be room for the rolls to expand in the dish. Cover with plastic wrap and let rise for 30-45 minutes until the rolls have expanded to touch each other.
Preheat the oven to 350°F. Bake the rolls for 30-35 minutes, until golden brown. Remove from the oven and let cool.
While the rolls cool, make the frosting. In a medium bowl, whip the softened butter until light and fluffy, about 2-3 minutes. Add vanilla extract and a pinch of salt. Add the confectioner's sugar and 1 Tablespoon milk, mixing until smooth. Add additional milk to reach your desired consistency, if needed. Spread the frosting on the rolls and serve.
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Notes
*You do not need to use a stand mixer to make this recipe. You can also make the dough in a large mixing bowl with a wooden spoon, then knead by hand.**If you are doubling or tripling this recipe, divide the dough into 2 (for doubling) or 3 (for tripling) portions. Then divide each portion into individual rolls and continue with the directions as written. To use active sourdough starter: Omit the commercial yeast and replace the sourdough discard with active starter (200g). You will also need to increase the rise times. To make overnight cinnamon rolls: Once you have shaped the cinnamon rolls and placed them in the baking pan, cover with plastic wrap and let rise in the refrigerator overnight. In the morning, remove from the fridge and let the rolls come to room temperature, about 2-3 hours. The rolls should look puffed and be touching each other in the pan.Pour ½ cup warm milk (any kind) or heavy cream over the rolls, then bake as directed. The additional warm milk will give the rolls a bit of extra moisture that will be soaked up into the dough while baking.