1Combine sourdough starter, water, and sugar, stirring to dissolve, then add flour, mix and knead into a dough ball.
2Cover the dough and leave it to rise overnight until it at least triples to quadruples in size.
3Cut the butter into half-inch blocks and set them on a plate to warm to room temperature.
4To the bowl of a stand mixer fitted with the dough hook attachment, add the flour, sugar, salt, warm milk, egg, and the sweet stiff starter.
5Mix on speed 2 for 3-5 minutes until the dough starts to clump around the dough hook.
6Turn the mixer off and let the dough rest for 30 minutes.
7Turn the mixer on speed 2 and start adding the room temperature butter, one pat at a time, waiting until that bit of butter is completely mixed into the dough before adding the next one. This process will take 7 to 10 minutes.
8After the butter is fully incorporated, mix on speed 3 for 1 to 2 minutes until the dough smooths and clings to the dough hook.
9Transfer the dough to a bulk fermentation container and cover.
10Let the dough rest for 30 minutes.
11Give the dough 3 sets of coil folds at 30-minute intervals.
12Allow the dough to bulk rise by about 50%, just until it is puffed up a bit.
13Place the bowl of dough in the fridge and chill for at least 4 hours or until evening.
14Line your pan with parchment paper.
15Divide the dough into sixteen 54g pieces and shape each into a tight ball.
16Cover and let rest for 1 hour, then tighten the shape of each dough ball into a tight circle and place the balls in the lined pan.
17Cover loosely with plastic wrap or a shower cap and refrigerate overnight.
18Take the pan out of the fridge and leave at room temperature for the rolls to puff up to double in size for their second rise. Depending on temperature, this can take anywhere from 4-8 hours.
19Preheat your oven to 400°F.
20Whisk together one egg and a splash of whole milk for the egg wash.
21Brush on the egg wash and sprinkle some flaky salt if desired.
22Bake for 10 minutes, then reduce the temperature to 350°F and bake for an additional 20 minutes.