In a large bowl, combine the flour, granulated sugar, salt, and yeast. Mix well. In a separate bowl, whisk together the warm milk, melted butter, egg, and vanilla extract. Pour the wet ingredients into the dry ingredients and mix until a dough forms. Knead the dough on a floured surface for about 5 minutes until smooth.
Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
While the dough is rising, prepare the cream cheese filling. In a medium bowl, beat together the softened cream cheese, powdered sugar, and lemon juice until smooth and creamy. Set aside.
Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
Once the dough has risen, punch it down and roll it out on a floured surface into a rectangle about 1/4 inch thick. Cut the dough into 6 equal squares.
Place a spoonful of the cream cheese mixture in the center of each square, then top with a few slices of fresh strawberries.
Fold the corners of each square towards the center to create a pocket, pinching the edges to seal.
In a small bowl, whisk together the egg and milk for the egg wash. Brush the tops of each Danish with the egg wash.
Bake in the preheated oven for 20-25 minutes, or until golden brown. Let cool slightly before serving.