Make the Blackberry Curd: In a saucepan over medium heat, combine blackberries and granulated sugar. Cook, stirring occasionally, until the berries break down and release their juices (about 5 minutes). Press the mixture through a fine-mesh sieve to remove seeds, returning the smooth puree to the saucepan. Whisk in the egg, egg yolks, and lemon juice. Cook over low heat, stirring constantly, until thickened (about 5–7 minutes). Remove from heat and stir in the butter until melted and smooth. Cover and chill the curd in the refrigerator for at least 30 minutes.

Prepare the Cream Cheese Filling: In a medium bowl, beat the cream cheese and sugar until smooth. Add the egg yolk and vanilla extract, mixing until combined.

Assemble the Danishes: Preheat the oven to 400°F (200°C). Line two baking sheets with parchment paper. Roll out the puff pastry sheets slightly and cut each into 4 equal squares (8 total). Place the squares on the prepared baking sheets. Score a smaller square about ½ inch from the edge of each puff pastry piece, being careful not to cut all the way through. Dock the center square with a fork to prevent it from puffing too much.

Fill the Pastry: Spoon a dollop of cream cheese filling into the center of each square and spread gently within the scored area. Top with a teaspoon of chilled blackberry curd.

Bake the Danishes: Brush the edges of the puff pastry with the egg wash and sprinkle with turbinado sugar. Bake for 18–22 minutes, or until the pastries are golden brown and puffed.

Garnish and Serve: Once cooled slightly, top each Danish with a fresh blackberry and dust with powdered sugar. Serve warm or at room temperature.