In a liquid measuring cup, measure out the warm water and dissolve the yeast
In a large bowl, whisk together the flour, sugar, salt, and lemon zest. Cut the cold butter into the flour mixture. Then incorporate the butter into the flour with your fingers until coarse crumbles form. Stir in the yeast/water mixture, the warmed milk, and the eggs.
Turn the dough out onto a well-floured surface and knead for about 2 minutes. The dough will be tacky. Add a little flour as needed while you knead the dough. Form the dough into a ball, place in a bowl, cover, and refrigerate for at least 2 hours or overnight.
Make your filling by stirring together the chopped apples, sugar, cinnamon, and melted butter.
When you are ready to bake, preheat the oven to 400°F and butter a baking sheet, or line with parchment paper.
Make the cream cheese filling by beating together the cream cheese, powdered sugar, egg yolk, vanilla, and salt.
Punch down the dough and divide it in half. Cover the half you aren't working with. On a floured surface, stretch and roll the dough into a rectangle that’s about 1/4-inch thick.
Cut the dough down the middle lengthwise, and then cut it into 8 squares.
Spoon a heaping tablespoon of the cream cheese mixture into the center of each square. Add a spoonful of the apples on top of the cream cheese.
Pinch the 4 corners of the dough towards the center and press them together. They will expand when baked but this gives each piece an edge and some shape.
Brush each piece with the egg wash, place 2 inches apart on the prepared baking sheet, and bake for 12-15 minutes.
Repeat with the 2nd half of the dough.
Cool the danish completely on a wire rack before serving.