Combine water and milk in a microwave-safe bowl and microwave for 30 seconds to warm.

Pour warm milk mixture into a small bowl and whisk in yeast and sugar until the yeast dissolves.

Let the yeast mixture stand for 5 minutes until foamy.

In a large bowl or stand mixer bowl, combine bread flour, whole wheat flour, wheat bran, and salt.

Cut in chilled butter until the mixture resembles a coarse meal.

Add yeast mixture and 1 egg to the flour mixture and stir to combine.

Knead the dough on a lightly floured surface until smooth, elastic, and slightly sticky, about 8-10 minutes. Alternatively, knead in a stand mixer on medium speed with a dough hook for about 5 minutes.

Shape the dough into a ball and place in a lightly greased bowl.

Cover with a tea towel and let it rise until doubled, about 1 to 1 1/2 hours.

Punch down the risen dough and divide into 8 equal pieces.

Roll each piece into a ball and place them 2 to 3 inches apart on parchment paper-lined baking sheets.

Cover with a tea towel and let the dough rise until doubled, about 1 hour.

Preheat oven to 350°F (175°C).

Beat together cream cheese, powdered sugar, salt, and vanilla in a bowl until well combined for the filling.

Use the bottom of a glass or small measuring cup to make indents in the center of each piece of dough.

Spoon the cream cheese filling evenly into each indent, smoothing the tops.

Beat the remaining egg with 1 tablespoon of water in a small bowl or cup to make an egg wash.

Brush the egg wash over the brioche dough, avoiding the filling.

Bake until light golden brown, about 20-25 minutes.

While the danishes bake, combine apricots with honey in a medium bowl until the apricots are well coated.

Remove danishes from the oven and place on a cooling rack.

Top each danish with a few glazed apricots.

For the icing, whisk together powdered sugar, vanilla, and just enough milk in a small bowl to achieve a glaze consistency.

Drizzle the icing over the slightly cooled danishes.

Serve warm or at room temperature.