SOURDOUGH CROISSANTS

Steps:

• Levain: On day 1 at night, mix together starter, flour, and water in a large bowl. Cover with a damp kitchen towel or a large plate and let stand at room temperature 8 to 10 hours.
• Dough: On day 2 in the morning, make a sponge: Dissolve levain in warmed milk, stirring or whisking to combine. Add 300 grams flour (2 1/4 cups) and mix to combine; sponge should feel like a thick batter. Let stand 30 minutes.
• Stir sugar and salt into sponge, then add remaining 275 grams flour (2 cups); stir to combine. Knead with floured hands on a lightly floured surface about 4 minutes. Wash and lightly oil bowl and return dough to it. Cover with a large plate or a damp kitchen towel. Let stand 30 minutes.
• With dampened hands, grab underside of dough, stretch it out, and fold it back over itself. Rotate bowl one quarter-turn. Repeat 6 times. Cover with cloth and let stand 30 minutes. Repeat folding process every 30 minutes until dough feels pillowy and elastic, and has increased in volume about 50 percent-a total of 6 to 8 times, 3 1/2 to 4 1/2 hours. Cover and let stand 1 hour, then refrigerate 30 minutes along with butter package (see step 5; this is so they have the same temperature and a similar texture, which makes them much easier to work with).
• Butter package: During last resting of dough, combine butter and flour in the bowl of a mixer and beat on medium speed to combine. Transfer to a piece of parchment, top with a second piece of parchment, and roll out to a 7-by-7-inch square. Transfer to a baking sheet and refrigerate 30 minutes (when ready, package should be waxy and pliable, not rock-solid).
• Turn rested and chilled dough onto a floured surface; let stand 10 minutes. Roll out to a 10-by-10-inch square. Place butter package in center of dough. Roll corners of dough out another 5 inches. Lift one side at a time over butter package, enclosing it in dough; pinch seams to seal. Give dough a few firm knocks along its seams with side of rolling pin.
• Roll dough out to an 8-by-24-inch rectangle. Fold into thirds like a letter (bottom 8 inches of dough up, then top 8 inches down over that). Turn so seam faces side; repeat this rolling and folding process once more. (If butter starts to ooze out, put dough on a baking sheet and refrigerate for 10 to 15 minutes before rolling out further.) Place folded dough on a baking sheet and refrigerate 30 minutes.
• Repeat rolling-and-folding process once more (the third turn). If time permits and you have energy, repeat one more time after another 30-minute rest in refrigerator. Roll dough out until it begins to spring back (this is just to get a jump-start on the final rolling), then transfer to a baking sheet lined with parchment. Cover and refrigerate at least 8 hours and up to 1 day. (It is possible to roll and shape after a shorter rest of about 4 hours, but the longer rest makes the dough easier to work with.)
• On day 3 in the morning, line 2 baking sheets with parchment. Place chilled dough on a floured surface and roll into a 23-by-16 1/2-inch rectangle. (If you find that it is springing back, or a lot of butter is oozing out, transfer to refrigerator for a few minutes. If small patches of dough break, exposing butter, sprinkle with some flour to cover and refrigerate briefly.) Trim edges straight. Starting at one short end, use a pizza or pastry wheel to cut dough in half lengthwise, so you have two 22 1/2-by-8-inch strips. (If your dough feels unwieldy, briefly refrigerate.) Cut each strip into 5 rectangles, each about 4 1/2-by-8 inches. Cut from one bottom corner to opposite top corner of each rectangle, creating two triangles.
• Arrange triangles on work surface, with shortest sides nearest you and long, pointed ends farthest from you. Gently stretch width of short ends slightly. Then roll croissants toward pointed ends, holding onto the points and gently tugging to elongate as you roll. Bend either end of croissants toward middle slightly to form crescent shapes. Place croissants on prepared baking sheets, spaced about 3 inches apart, tucking points under shaped crescents so they don't unfurl in the oven. (You should be able to fit 10 on each half sheet pan.)
• Drape with plastic wrap and let stand at room temperature until puffed, expanded by about 60 percent, and very soft, 2 to 3 hours. (Or, if you are shaping the night before baking, place all the croissants on a single baking sheet and refrigerate overnight, as they won't really expand much. Remove about 3 hours before you want to bake, divide them between 2 sheets, and allow to proof as above; it could take slightly longer, given that they are cold.)
• Preheat oven to 400°F. Whisk together egg yolks and cream. Brush proofed croissants evenly with egg wash and bake, rotating pans from top to bottom and back to front halfway through, until puffed, golden brown, and baked through, 25 to 28 minutes. Let cool on sheets on wire racks 15 minutes, then transfer directly to racks and let cool completely. (Croissants are excellent the day they're made, but if making ahead, let cool completely, then freeze in resealable plastic bags. To serve, wrap in parchment-lined foil and reheat from frozen in a 350°F oven until just heated through, about 10 minutes.)