In a mixing bowl, combine the active sourdough starter, all-purpose flour, sugar, salt, milk, and water. Knead the dough until smooth and elastic. Allow it to rest for 30 minutes.
Roll out the cold unsalted butter into a square. Place the butter square on the dough and fold the dough over it, enveloping the butter completely. Roll out the dough-butter combination into a rectangle.
Perform a series of tri-folds and book-folds to create the iconic layers in croissants. Chill the dough between each fold to maintain the integrity of the butter layers.
Roll out the dough and cut it into triangles. Roll each triangle into a croissant shape, tucking the ends underneath. Place the shaped croissants on a baking sheet, cover, and let them proof until puffy.
Preheat your oven to 400°F (200°C). Brush the proofed croissants with an egg wash and bake until golden brown and flaky, typically around 20-25 minutes.
Allow the freshly baked sourdough croissants to cool slightly before indulging in the buttery, flaky goodness that awaits.
