Prepare the cheesecake filling by beating cream cheese until smooth, then gradually adding granulated sugar and vanilla extract. Spoon mixture into ice cube trays, press down gently, and freeze for at least 1 hour.

In a medium saucepan, combine diced strawberries with sugar over medium heat. Mash the fruit as it cooks, allowing it to thicken for about 45 minutes. Let cool completely.

In a large bowl, whisk together flour, baking powder, baking soda, and salt. In another bowl, cream softened butter and sugar until fluffy. Add egg and vanilla, mixing well. Gradually incorporate dry ingredients.

Fold cooled strawberry jam into cookie dough, mixing gently to create pockets throughout.

Preheat oven to 350°F (175°C). Flatten cookie dough in palm, place cheesecake disc in the center, gather edges, and shape into discs. Roll in sugar for finishing touch.

Arrange cookies on a parchment-lined baking sheet and bake for 11-12 minutes until golden. Press each cookie with a round cutter for neat shapes while warm.

Transfer baked cookies to a wire rack to cool completely. Dust with powdered sugar before serving, optionally alongside fresh strawberries or mint leaves.