Preheat your oven to 350 degrees F. Line a baking sheet with parchment paper.
In the bowl of an electric mixer fitted with a whisk attachment, beat the cream cheese until soft and creamy. Add in the sugar and vanilla and mix to combine.
Use a spatula to fold in the jam gently.
Unroll the sheet of puff pastry and use a knife to cut it into four squares. Divide the strawberry cream cheese mixture between the four squares.
In a small bowl, beat together an egg and a tablespoon of water to make the egg wash. Brush three sides of the dough with the egg wash. Fold the dough over to make a rectangle.
Use a fork to seal the edges. Transfer to the prepared baking sheet. Brush the pastries with the egg wash.
Bake the danishes for 15-20 minutes until golden brown.
To make the icing, combine the powdered sugar and ham. Add a little milk to thin the icing without making it too runny.
Remove the danishes to a cooling rack and let cool for 3-4 minutes before drizzling with the icing.