Put lukewarm milk and water in a large mixing bowl and dissolve fresh yeast and sugar in it.
Add salt and flour in portions and knead into a very soft dough.
Knead 40 g of butter into the dough in pieces and knead the dough for about 10 minutes to make it elastic and smooth. Cover the mixing bowl with the dough with plastic wrap and let the dough rise in the refrigerator for at least 4 hours or overnight (max. 10 hours).
Fold the baking paper into an envelope of about 20 cm x 20 cm, put 250 g of cold butter cut into thin slabs into it and roll it out with a rolling pin so that it is evenly distributed in the envelope. Put the butter plate in the envelope also in the refrigerator while the dough is rising.
Dust the work surface with flour and roll out the dough into a rectangle about 21 cm x 41 cm (that is, slightly larger than twice the size of the butter plate).
Take the butter plate out of the baking paper envelope and place it on one side of the rolled out dough rectangle, leaving a border about 1 cm wide (as shown in the pictures here above). Cover the butter plate with the second half of the dough and press the edge of the dough down on all sides.
Roll out the buttered dough into a long rectangle, fold in one of the shorter sides of the square about 2/3 to the center, fold in its second side about 1/3 to the center as well, and glue the two sides together. Now fold the dough from the two folded sides together like a book, wrap it in baking paper or plastic wrap, and chill it for 1 hour.
Roll out the dough sheet again on the floured work surface into a long rectangle, fold one of the shorter sides of the square in half on the center and place the second short side over it. Wrap the dough sheet again in baking paper or plastic wrap and chill for 1 more hour.
Roll out the dough on the floured work surface to 0.4-0.5 cm thick into a long rectangle (29 cm x 72 cm for me) and cut it from the shorter side into strips about 8 cm wide (9 strips for me). Cut each strip into two triangles (18 triangles for me), cut each triangle about 1 cm deep in the center on the short side, and roll it up from that side toward the tip.
Slightly bend the croissants lengthwise into a crescent shape and spread them out on two baking sheets lined with parchment paper, spacing them generously apart. Cover them with plastic wrap and let them rise at room temperature for about 1.5 hours.
First, carefully brush the croissants on the first baking sheet with beaten egg and let them dry for 5 minutes. Bake them in the preheated oven at 200 °C top and bottom heat for 10 minutes, then switch the oven to 180 °C top and bottom heat and bake them for another 10 minutes. Repeat the same with the croissants on the second baking tray.