Prepare the cheesecake filling by combining cold cream cheese, 3 tablespoons of granulated sugar, and ½ teaspoon of vanilla in a mixing bowl. Whip until fluffy, about 3-4 minutes. Freeze for at least 1 hour.
Make the blueberry jam by combining fresh blueberries and ¼ cup of granulated sugar in a saucepan. Cook on medium heat for about 40 minutes, mashing the blueberries as they cook. Cool the jam in the fridge.
Prepare the cookie dough by whisking together flour, baking powder, baking soda, and salt. In a separate bowl, combine granulated sugar and lemon zest. Cream together with softened butter until light and fluffy. Add egg and vanilla, mixing until pale and fluffy, then gradually incorporate dry ingredients.
Assemble the cookies by flattening a portion of dough, adding blueberry jam, and covering it with another portion of dough. Seal the edges gently and place on a baking sheet.
Preheat the oven to 350°F (175°C). Roll each dough ball in granulated sugar and bake for 11-12 minutes until edges are golden. Cool on a baking sheet for 10 minutes.