Feed the starter. Mix the starter, flour, and water at a ratio of 1:3:3 in a small jar until combined. Leave at room temperature overnight until doubled and bubbly. If your kitchen is warm, use 1:5:5 so it rises more slowly. 20 g starter, 60 g all-purpose flour, 60 g water
Day 1
Mix the dough. Whisk the active levain into the water in a large bowl until loosened. Add the flour, sugar, and salt and mix until a dough forms, about 3-4 minutes. 220 g water, all the sourdough starter, 450 g all-purpose flour, 50 g sugar, 8 g salt
Tip onto the bench, add the softened butter, and knead until fully incorporated and smooth. Shape into a ball, place in a lightly greased bowl, cover, and ferment at room temperature (ideally 23-25°C/74-77°F) for 3-5 hours until risen by 30-40%. 40 g unsalted butter
Chill the dough. Press the dough into a flat rectangle. Wrap tightly in parchment or plastic wrap and refrigerate for at least 2 hours.
Make the butter packet. Slice the cold butter and arrange the pieces in a grid on a sheet of parchment paper. Place a second sheet on top and bash and roll into an even, flat block. Fold the parchment edges in to create a neat 15x20cm (6x8 inch) frame and press the butter to fill it evenly. Refrigerate until cold. If using the flour method, soften the butter first, mix in 1½ tablespoons of flour, then roll between the parchment sheets into the same size rectangle. 250 g unsalted butter
Encase the butter. Remove the butter from the fridge and give it a few firm bashes with the rolling pin to make it pliable again. Check that it's cold but also nice and bendy and doesn't break.
Roll the chilled dough on a lightly floured bench into a 20x30cm (8x12 inch) rectangle. Place the butter in the centre. Fold the top third down and the bottom third up to encase it. Pinch the edges firmly to seal. Score a shallow slit along each long edge to relieve tension. Turn the dough 90 degrees.
Roll and fold. Using a rolling pin, press across the dough first to start dispersing the butter, then roll to around 8mm thick, focusing on length rather than width. Always roll away from you in one direction; rolling back and forth drags the layers in opposite directions and smears the butter. Check it's not sticking and dust lightly with flour if needed. Trim the uneven short ends to expose the layers, then brush off any excess flour. Fold the bottom third up and the top third down (a letter fold). Wrap and refrigerate 30 minutes.
Repeat twice more. Take the dough from the fridge and rotate it 90 degrees from how it was last folded. Before rolling, gently press the rolling pin across the surface of the dough to test how it responds. You are not trying to flatten it, just checking whether it gives slightly. If it feels completely solid, leave it on the bench for 5 minutes before continuing.Roll to 8mm thick, trim uneven edges, brush off flour, and letter-fold again. Wrap and refrigerate 30 minutes. Repeat one final time for three folds total. Note: if the butter shatters when you start rolling, it's too cold; leave the dough on the bench for 5-10 minutes. If the butter feels soft or greasy, refrigerate it immediately. After the third fold, wrap tightly and refrigerate for at least 8 hours, or overnight.