Mix the Dough: To the bowl of a stand mixer fitted with a dough hook, add sourdough discard, water, milk, instant yeast, granulated sugar, melted butter, salt, and bread flour. Knead on low to medium speed for about 8–10 minutes until you have a smooth, cohesive, and strong dough. The dough should feel tacky but not sticky; if it’s too sticky, add bread flour 1 tablespoon (8–9 grams) at a time until it reaches the right consistency. If kneading by hand, work the dough for 12 to 15 minutes, until smooth and strong.

First Rise: Place the dough in a container and cover it with plastic wrap. Let it rise in a warm spot until doubled in size, about 1 to 1½ hours if the dough is kept warm.

Make the Butter Block: While the dough rises, prepare the butter block. Tear off a 28-inch sheet of parchment paper and fold it using a ruler to create a 9x12-inch rectangle pocket. Slice the 340 grams of butter into six equal rectangular pieces and arrange them in a line inside the parchment. Fold the paper back over the butter and flip it over. Pound the butter a few times with a rolling pin, then roll from the center outward until the butter is pliable and evenly fills the 9x12-inch space. Chill the butter block for at least 2-3 hours or for a couple of days, until firm but still pliable.

Roll and Chill Dough: Once the dough has doubled in size, dump it out on the counter and roll and pat it into a 12 by 18-inch rectangle. Place the dough on a half sheet (18 by 13 inch) baking sheet and pull the dough evenly to the corners of the baking sheet if needed. Cover with plastic wrap and refrigerate for about 4 hours.

Laminate the Dough: Remove both the butter block and the dough from the refrigerator. Lightly flour your work surface and take the chilled dough out of the pan. Gently roll it into a 12x18-inch rectangle. Unwrap the butter block from the parchment paper and confirm that the dough and butter are about the same pliability. Turn the parchment paper over to release the butter block onto the center of the dough. Fold each side of the dough over the butter so the edges meet in the center, like folding a letter. Pinch the seams to completely seal the butter inside the dough.

First Fold: Place the dough seam-side down with the 12-inch side vertical and the 6-inch side horizontal. Starting in the center, press gently with a rolling pin to make small indentations, moving upward and downward to help soften and spread the butter evenly inside the dough. Roll the dough into a 10 by 20-inch rectangle. Chill: Trim the edges with a sharp knife so they are neat and straight, then fold the dough in thirds, like folding a letter, to form a 10 by 6-inch rectangle. Wrap the dough in plastic wrap and chill in the refrigerator for about 1 hour.

Second Fold: After the dough has chilled and rested to about 60ºF, remove it from the refrigerator or freezer. Place the dough seam-side down with the 6-inch side horizontal and the 10-inch side vertical. Press gently in the center with the rolling pin to loosen the butter, then roll evenly from the center outward, flipping and rotating as needed, until the dough measures about 10 by 20 inches. Trim the edges neatly with a sharp knife, fold in thirds to form another 10 by 6-inch rectangle, then wrap well and chill for 1 hour in the refrigerator.

Roll and Shape: Roll the chilled dough into a 24 x 12-inch rectangle, about ¼–½ inch thick. Trim the edges neatly with a sharp knife to square off the dough. For smaller croissants, cut the dough into long triangles about 3 inches wide at the base and 12 inches long. For larger croissants, cut the triangles about 6 inches wide at the base and 12 inches long. To shape, gently stretch the base of each triangle, then roll it up from base to tip without pressing down, finishing with the tip tucked underneath.

Chill Overnight: Cover the shaped croissants lightly with plastic wrap and place them in the refrigerator overnight.

Proof: Remove the shaped croissants from the refrigerator and allow them to proof until doubled in size, puffy, jiggly, and with visible layers.

Bake: Preheat the oven to 375ºF. In a small bowl, whisk together one egg with a splash of cream and a pinch of salt to make an egg wash. Gently brush the croissants, taking care to avoid the cut edges. Bake for 30–35 minutes, rotating the pans halfway through, until the croissants are deeply golden brown and flaky.