Whisk the flour, sugar, yeast, and salt together in a large bowl.

Add the cold milk, egg, vanilla extract, and softened butter. Mix until a shaggy dough forms.

Knead the dough for 4 to 5 minutes, until smooth. Avoid over-kneading; the dough does not need the extended kneading time you would use for a traditional bread dough.

Shape the dough into a rectangle, wrap tightly, and refrigerate for at least 1 hour, or until thoroughly chilled.

Pound and roll the butter into approximately a 6 × 8-inch rectangle.

The butter should be cold but pliable. When you gently bend the parchment, the butter should bend with it rather than cracking or snapping.

Refrigerate briefly if the butter becomes too soft.

Roll the chilled dough into approximately an 8 × 16-inch rectangle.

Place the butter block over the bottom half of the dough. Fold the top half of the dough over the butter and gently seal the edges to enclose it.

Rotate the dough 90 degrees.

Carefully roll it into approximately an 8 × 18-inch rectangle.

Fold the dough into thirds like a business letter. Wrap and refrigerate for 30 minutes.

Repeat the rolling and letter-fold process two more times, refrigerating the dough for 30 minutes between each fold, for a total of three letter folds.

Beat the cream cheese and sugar together just until smooth.

Add the flour and mix until incorporated.

Add the egg yolk, vanilla extract, and salt and mix just until combined.

Refrigerate the filling while you roll and shape the dough.

Line baking sheets with parchment paper.

Roll the chilled Danish dough on a lightly floured surface to approximately ⅓ inch thick, or slightly thinner. If the pastries are too thin, they will be deflated, but if they are too thick, they won’t bake fully internally.

As you roll, periodically lift the dough from the work surface to make sure it is not sticking or becoming overly stretched. If the dough begins shrinking back significantly, cover it and let it rest for 5 to 10 minutes before continuing.

Using a 4-inch round cutter, cut rounds from the dough.

Gather the scraps gently, allow them to rest for a few minutes, then reroll and cut additional rounds. At this point, the dough can be hard to roll, and it will continue to spring back. Give it small intervals in between rolling to ensure it’s not going to shrink once you cut the rounds.

Arrange the rounds on the prepared baking sheets.

Using a 2-inch round cutter, gently press an indentation into the center of each round without cutting all the way through the dough.

Cover the shaped pastries loosely and let them rise at room temperature for 60 to 90 minutes, or until visibly puffy.

The Danish will not necessarily double in size, but the dough should look noticeably swollen and the laminated layers should become more apparent. The surface of a danish should feel fluffy and spring back when touched.

Avoid proofing the pastries in a very warm environment. A room temperature of about 72 to 75°F is ideal.

Toward the end of the proofing time, preheat the oven to 400°F (205°C) for at least 30 minutes.

Whisk the egg and milk together to make the egg wash.

Brush the exposed dough lightly with the egg wash, avoiding the cut edges as much as possible.

Bake the Danish at 400°F (205°C) for 8 minutes.

Without opening the oven unnecessarily, reduce the oven temperature to 375°F (190°C) and continue baking for another 10 to 14 minutes, or until the pastries are deeply golden brown.

The bottoms should also be golden and crisp.

Transfer the pastries to a cooling rack and let cool for at least 15 minutes before serving.

Whisk the powdered sugar with 1 tablespoon of milk until smooth. Add more milk, a little at a time, until the glaze reaches a thick but pourable consistency.

Drizzle over the Danish once they have cooled for at least 15 minutes.