Whisk lukewarm milk, warm water, yeast, and 15 ml of sugar in a bowl. Let stand for 5 to 10 minutes until frothy.

In a stand mixer fitted with a dough hook, combine the flour, remaining sugar, salt, egg, and yeast mixture. Knead on low speed for 5 to 7 minutes until a smooth, slightly tacky dough forms. Wrap tightly in plastic wrap and chill for 2 hours.

Place the cold butter between two sheets of parchment paper and beat with a rolling pin to form a flat 7-inch square of uniform thickness. Chill for 15 minutes to keep it pliable but firm.

Roll the chilled dough on a lightly floured surface into an 11-inch square. Place the butter block diagonally in the center, fold the four corners of dough over the butter to enclose it completely, and pinch the seams shut.

Roll the dough into a 16x8-inch rectangle. Fold the top third down and the bottom third up like a business letter (first turn). Wrap and chill for 45 minutes. Repeat this rolling, folding, and resting process two more times for a total of three turns.

Roll the laminated dough to 1/2-inch thickness. Using a 3-inch round cutter and a 1-inch center cutter, cut out doughnut rings. Transfer to a parchment-lined baking sheet, cover loosely with a damp towel, and proof at room temperature for 1 to 1.5 hours until puffy.

Heat frying oil in a deep heavy-bottomed pot to 177 °C (175 °C). Carefully drop 2 to 3 dough rings into the hot oil at a time. Fry for 90 seconds per side until deep golden brown and crisp throughout.

Remove cronuts with a slotted spoon, drain on wire racks for 1 minute, then immediately toss in cinnamon sugar while warm. Let cool to room temperature before filling.

Fit a piping bag with a small round tip and fill with chilled vanilla pastry cream. Poke 4 small holes around the top perimeter of each pastry, pipe pastry cream inside, and top with a light drizzle of glaze if desired.