In a medium saucepan, combine fresh blueberries with sugar, and cook over medium heat, stirring gently. Allow it to simmer for about 10-15 minutes until thickened. Set aside to cool.

In a mixing bowl, beat together cream cheese and sugar until smooth and creamy. Incorporate vanilla extract, then refrigerate to chill.

In a large bowl, whisk together all-purpose flour, baking powder, and salt. Cream softened butter with sugar and lemon zest until fluffy. Beat in the egg, then gradually add dry mixture until combined.

Wrap prepared dough in plastic wrap and refrigerate for 30 minutes to prevent excessive spreading during baking.

Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper. Roll chilled dough into small balls, flatten slightly, then add cheesecake filling and blueberry jam. Seal edges around filling.

Bake for 12-15 minutes until edges are golden and centers appear puffed. Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.