Prepare the Dough:

• In a mixing bowl, combine warm water and warm milk. Sprinkle the active dry yeast over the liquid and let it sit for about 5 minutes until it becomes frothy.
• In a separate large bowl, whisk together the all-purpose flour, granulated sugar, and salt.
• Add the yeast mixture, large egg, and vanilla extract to the dry ingredients. Mix until a soft dough forms.
• Knead the dough on a lightly floured surface for about 5 minutes until it becomes smooth and elastic.
• Shape the dough into a ball, place it in a lightly greased bowl, cover, and let it rise in a warm place for about 1 hour or until doubled in size.

Laminate the Dough:

• On a lightly floured surface, roll out the risen dough into a large rectangle, approximately 10×15 inches.
• Take the cold unsalted butter and cut it into thin slices. Arrange the butter slices evenly over two-thirds of the dough rectangle.
• Fold the unbuttered third of the dough over the middle third, then fold the remaining third over the top, similar to folding a letter.
• Rotate the dough 90 degrees, roll it out again into a 10×15 inch rectangle, and repeat the folding process.
• Wrap the folded dough in plastic wrap and refrigerate for at least 30 minutes. Repeat the rolling and folding process two more times, chilling between each fold.

Prepare the Cinnamon Filling:

• In a small bowl, mix together the softened unsalted butter, brown sugar, and ground cinnamon until well combined.

Assemble the Pastries:

• After the final chill, roll out the laminated dough into a rectangle about 1/4 inch thick.
• Spread the cinnamon filling evenly over the dough, leaving a small border around the edges.
• Starting from one long edge, roll the dough tightly into a log.
• Using a sharp knife, cut the log into 1-inch thick slices.
• Place the slices onto a baking sheet lined with parchment paper, spacing them apart to allow for expansion.
• Cover the pastries lightly and let them rise for about 30 minutes.

Bake:

• Preheat the oven to 375°F (190°C).
• Bake the risen pastries for 15-20 minutes, or until they are golden brown and flaky.
• Remove from the oven and let them cool slightly on a wire rack.

Glaze:

• In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
• Drizzle the glaze over the warm pastries before serving.