In a large bowl, combine the flour, sugar, yeast, and salt. Add the warm milk, warm water, and eggs, then knead until the dough is smooth and elastic. Cover and let it rest for 30 minutes.
Roll the dough into a rectangle. Place the cold butter in the center and fold the dough over it, sealing the edges.
Roll out the dough and fold it into thirds. Repeat this process 3-4 times, chilling the dough for 30 minutes between folds.
After the final fold, wrap the dough in plastic wrap and refrigerate overnight (or at least 8 hours).
Roll the dough to ½-inch thickness. Use a round cutter to cut out donut shapes, then use a smaller cutter to create the center hole.
Place the cut dough on parchment paper and let it proof in a warm place for 1-2 hours, or until slightly puffed.
Heat vegetable oil in a deep fryer or large pot to 350°F (175°C).
Carefully lower the dough pieces into the hot oil, frying 1-2 at a time. Cook for 1-2 minutes per side, until golden brown. Remove and drain on a paper towel-lined plate.
Use a piping bag fitted with a small tip to fill each Cronut with pastry cream.
Roll in powdered sugar, drizzle with glaze, or add sprinkles for a festive touch.