In the bowl of a stand mixer, combine the warm milk, sourdough starter, granulated sugar, and egg. Whisk until well combined.

Add the bread flour and salt to the wet ingredients. Attach the dough hook and mix on low speed for 2-3 minutes until a shaggy dough forms. Scrape down the sides of the bowl.

Increase speed to medium-low and knead for 5 minutes. Begin adding the softened butter, one cube at a time, allowing each cube to incorporate before adding the next. This process should take about 5-7 minutes. Continue kneading for another 5-7 minutes until the dough is smooth, elastic, and passes the windowpane test (you can stretch a small piece thin enough to see light through it without tearing).

Transfer the dough to a lightly oiled large bowl. Cover with plastic wrap or a tight-fitting lid and let it rest at room temperature (70-75°F / 21-24°C) for 2-3 hours, performing a set of stretch and folds every 30-45 minutes (gently pull a portion of the dough up and fold it over itself, rotating the bowl a quarter turn and repeating 3-4 times).

After the stretch and folds, refrigerate the covered dough for at least 12 hours, or up to 24 hours. This slow cold fermentation develops flavor and makes the dough easier to handle for shaping.

Lightly grease a 12-cup muffin tin (or use paper liners). Take the cold dough out of the refrigerator. Lightly flour your work surface and the dough.

Roll out the dough into a large rectangle, about 24x18 inches (60x45 cm) and very thin (about 1/16 inch / 2mm thick). If the dough resists, cover it and let it rest for 10-15 minutes before continuing to roll.

Evenly brush the melted butter over the entire surface of the rolled-out dough, leaving about a 1/2-inch border on one of the longer sides. Sprinkle the granulated sugar evenly over the butter, followed by the chocolate chips.

Starting from the longer side without the border, carefully roll up the dough tightly into a log. Press the seam to seal it.

Using a sharp knife or bench scraper, cut the log in half lengthwise to create two long strips. You will have two strips, each with the layers exposed.

Take one strip and carefully twist it into a spiral, keeping the cut sides facing outwards. Coil the twisted strip into a 'cruffin' shape and place it into one well of the prepared muffin tin. Repeat with the second strip and the remaining cruffins. You'll make 6 cruffins this way (from 12 strips, 2 strips per cruffin). For 12 cruffins, you'll need to roll, butter, sugar, chocolate, and cut 2 separate logs of dough.

Cover the muffin tin loosely with plastic wrap or a clean kitchen towel. Let the cruffins proof at room temperature for 2-4 hours, or until they have visibly puffed up and are soft and jiggly. The exact time will depend on your room temperature and starter activity. They won't double, but should look noticeably larger and airy.

Preheat your oven to 375°F (190°C) during the last 30 minutes of proofing.

Bake the cruffins for 20-25 minutes, or until deeply golden brown and cooked through. If they are browning too quickly, you can loosely tent them with foil.

Remove from the oven and let cool in the muffin tin for 5-10 minutes before transferring them to a wire rack to cool completely.

While the cruffins cool, whisk together the powdered sugar and milk/water in a small bowl until smooth. Drizzle the glaze over the cooled cruffins just before serving.