Combine the dough ingredients (water, milk, baking yeast, flour, sugar, salt and butter) and knead for 5 min. Shape the dough like a disc and leave in the fridge overnight.
Put some flour on your work surface to prevent the dough from sticking. With a rolling pin, roll out the dough into a 25×25 cm rectangle and pound butter until it’s about 15×15 cm. Put it on top of the dough on the center.
Fold the 4 flaps of the dough over the butter.
Roll out the dough to a 50×20 cm rectangle. Fold one third of the dough on top of itself and then fold the over side over it. Leave in fridge for 20 min. Repeat step 3 two more times.
Roll the dough into a 3 mm thick rectangle. Cut 12×18 cm triangles and roll them starting from the base to the thiner part (the peak).
Arrange the shaped croissants on baking sheets and let rest for 2-3h until doubled in bulk.
Preheat the oven to 210°C. Brush the rolls with the beaten egg and bake for 20 min and allow the croissants to cool completely on a rack.
Using a syringe and from the top, inject the salted butter caramel inside the croissants.