In a medium pot, combine fresh blueberries, granulated sugar, lemon juice, vanilla extract, and cornstarch. Cook over moderate heat for 30-40 minutes, stirring gently until thickened.

In a separate bowl, whisk together flour, baking powder, and salt. Set aside.

In a large bowl, beat the softened butter with sugar until fluffy, about 2-3 minutes.

Add the egg and vanilla extract, mixing until well-blended, about 2 more minutes.

Gradually add dry ingredients to the wet mixture, mixing on low until just combined.

Gently fold in the cooled blueberry jam into the cookie dough.

Preheat the oven to 350°F (175°C). Scoop the dough onto parchment-lined baking sheets, sprinkle with sugar if desired, and bake for 10-13 minutes.

Cool on the baking sheet for 5 minutes before transferring to a wire rack.