Heat the milk in a small saucepan over medium heat until it reaches 180℉. Hold at 180℉ for one minute. Transfer ¼ cup (60 grams) of the scalded milk to the bowl of a stand mixer. Reserve the remaining ½ cup (120 grams) in the pot.
¾ cup (180 grams) whole milk
Make tangzhong by adding ¼ cup (30 grams) of flour to the reserved milk in the saucepan. Whisk over low heat until the mixture is thick and resembles mashed potatoes.
4 ¼ cups (510 grams) all-purpose flour
Transfer the tangzhong to the stand mixer bowl with the rest of the milk. Add the ice water and eggs, and whisk until mostly combined. Add the remaining flour (4 cups or 480 grams) and sourdough starter to the bowl. Attach the dough hook and knead on low speed until the mixture just comes together. Cover and let rest for 5 minutes.
4 ¼ cups (510 grams) all-purpose flour, ¼ cup (60 grams) ice-cold water, 3 large (150 grams) cold eggs, ½ cup (100 grams) sourdough starter discard
Add the sugar and salt to the mixture. Knead on medium-low speed for 20 minutes, or until the dough cleanly pulls away from the sides of the bowl. With the mixer running on low to medium-low speed, add the softened butter one tablespoon at a time, allowing each piece to fully incorporate before adding the next. The dough may separate but will come back together.
¼ cup (50 grams) granulated sugar, ½ teaspoon kosher salt, ½ cup (113 grams or 1 stick) unsalted butter
Transfer the dough to a clean bowl, cover, and let it rise at room temperature until doubled in size (about 6-8 hours in a 70-75℉ kitchen, but this can vary).
Once the dough has doubled, refrigerate it overnight or for at least 8 hours. This is necessary to be able to roll it out.
Prepare the filling by mixing the softened butter, brown sugar, and cinnamon in a bowl. Cover and refrigerate overnight. Remove from the fridge 1-2 hours before using to soften.
4 tablespoons (57 grams) unsalted butter, ½ cup (100 grams) brown sugar, 4 teaspoons ground cinnamon
Day 2:
Butter and line the bottom of a 9" x 13" baking pan with parchment paper. On a lightly floured surface, roll out the chilled dough into a ¼-inch thick, 12-inch by 20-inch rectangle. Use enough flour to prevent sticking.
Spread the prepared filling out into a thin, even layer over the dough, leaving a 1-inch border on one long edge. Roll the dough tightly into a log starting from the long edge with filling to the border.
Trim the tapered ends and cut the log into 15 rolls, about 1 ¼ inch thick each. Place the rolls in the prepared baking pan.
Cover and let proof for 1 ½ to 2 hours, or until puffy.
Preheat the oven to 375℉ about 20 minutes before proofing is complete. Cover the pan with buttered aluminum foil and bake for 15 minutes. Uncover and bake for an additional 10-15 minutes until lightly golden brown. Allow rolls to cool for 5 minutes before icing.
Whisk together powdered sugar, melted butter, milk, and vanilla extract in a mixing bowl. Pour the icing over the warm cinnamon rolls and spread evenly with a knife.