Make the sweet stiff starter: Combine the sweet stiff starter ingredients together, stir until all the flour is hydrated, the mixture may appear a little dry. Continue mixing until it comes together into a shaggy dough. Transfer the starter to an airtight container, set it in a warm place, and let the starter activate overnight.
60 grams all-purpose flour, 28 grams water, 14 grams cane sugar, 14 grams sourdough starter
Make the dough: Whisk the eggs, milk, and sugar together in a large mixing bowl until no traces of egg whites remain.
2 eggs, 113 grams whole milk, 36 grams cane sugar
Tear the sweet stiff starter into small pieces and add it into the large mixing bowl with the flour and salt. Stir all the ingredients together until the mixture looks like a cohesive dough.
270 grams all-purpose flour, 6 grams salt
Knead the butter into the dough one tablespoon at a time, wait until each portion is incorporated before adding more. Cover the bowl with plastic wrap and let it rest for 1 hour.
56 grams unsalted butter
Strengthen the dough: Turn the dough out on a lightly floured work surface and knead until it appears smooth and elastic. Round the dough into a tight ball and place it into a clean, lightly-greased bowl.
First rise: Cover the bowl with plastic wrap and let it rise in a warm spot until doubled in volume, about 4 to 6 hours.
Shape the dough: Line an 8-inch square baking pan and line it with parchment paper. Divide the dough into 9 portions. Round each piece of dough into a tight ball and arrange them in your prepared pan.
Second rise: Cover the baking pan with plastic wrap and transfer the dough to the refrigerator and proof overnight (8 to 16 hours).
Prep: Remove the rolls from the refrigerator and set them on the counter. Preheat the oven to 350 F.
Egg wash: Once the rolls look ready (they should look well risen, fluffy and fill the pan), beat the egg to make your egg wash. Using a pastry brush, brush the tops of the dough with egg wash.
1 egg
Bake: Bake the rolls for 20 to 25 minutes or until the rolls are golden brown and register at least 190 F when probed with an instant-read thermometer.
Brush with butter: Remove the baked rolls from the oven and brush them with melted butter.
28 grams unsalted butter
Enjoy and store: These rolls are best enjoyed on the day they are baked. Store leftover rolls in an airtight container at room temperature for up to 3 days.