Step 1: Prepare the Blackberry Curd

1. Preheat the oven to 400°F (200°C). Line two baking sheets with parchment paper.
2. Puree the blackberries until smooth. Strain the mixture through a fine-mesh sieve to remove seeds, then discard the seeds.
3. Transfer the strained blackberry puree to a medium saucepan and heat over medium heat until simmering. Reduce the heat to low and continue simmering until the mixture reduces to ½ cup, about 20 minutes. Stir occasionally to prevent burning.
4. Remove from heat and let cool slightly.
5. In a separate bowl, whisk together the reduced blackberry puree, sugar, whole egg, egg yolks, and lemon juice.
6. Pour the mixture back into the saucepan and heat over medium-low, stirring constantly. Simmer until the curd thickens, about 5 minutes.
7. Remove from heat and whisk in the butter until fully melted and incorporated.
8. Strain the curd again through a fine-mesh sieve for a silky texture. Set aside and let cool.

Step 2: Make the Cream Cheese Filling

1. In a mixing bowl, beat together the softened cream cheese, sugar, egg yolk, and vanilla extract until smooth and creamy.
2. Set aside while you prepare the puff pastry.

Step 3: Prepare the Puff Pastry

1. Lightly dust a clean work surface with flour to prevent sticking.
2. Roll out the puff pastry sheets slightly to ensure an even thickness.
3. Use a round cutter or a glass to cut 3 rows of 3½-inch circles, yielding 9 pieces per sheet (18 total).
4. Arrange the puff pastry rounds on the prepared baking sheets, spacing them slightly apart.

Step 4: Assemble the Danishes

1. Use a fork to prick the center of each pastry round to prevent excessive puffing while baking.
2. Place about 1 tablespoon of the cream cheese filling in the center of each round, leaving a border around the edges.
3. Brush the edges of each pastry with the egg wash to encourage a golden-brown color.
4. Sprinkle about 1 teaspoon of turbinado sugar around the edges for extra crunch and caramelization.

Step 5: Bake the Danishes

1. Place the baking sheets in the preheated oven and bake for 15 to 18 minutes, or until golden brown and puffed.
2. Rotate the baking sheets halfway through baking to ensure even browning.
3. Remove from the oven and allow the pastries to cool completely before adding the blackberry curd.

Step 6: Fill and Garnish

1. Spoon about 1 heaping tablespoon of the blackberry curd into the center of each cooled pastry.
2. Top with fresh blackberries for added texture and freshness.
3. Lightly dust with powdered sugar for a beautiful finishing touch.