Warm the milk (should not be boiling) and add 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. Increase speed to medium for 2 minutes until a smooth dough ball forms; you can also knead by hand. The dough should be smooth, soft, and just slightly 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 small bowl of warm water. This will help them plump up before baking.
After the first rise, transfer the dough to a floured surface. Roll the dough into a 12x18-inch rectangle**. Drain the raisins. Spread the dough with softened butter and evenly sprinkle with brown sugar, drained raisins, and cinnamon.
From the long end of the rectangle, roll the dough into a log, pressing the seam at the end 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 30-45 minutes until the rolls have expanded to touch each other. If they need some more time to reach that point, let them rise a little longer! (See notes below if making overnight cinnamon rolls).
Preheat the oven to 350°F. Bake the rolls uncovered for 30-35 minutes, until golden brown.
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. With the mixer on low, slowly add the confectioner's sugar and 1 Tablespoon milk. Mix until smooth. Add additional milk to reach your desired consistency, if needed. Smooth the frosting on the rolls and serve immediately.