Prepare the cheesecake filling by beating cold cream cheese with sugar and vanilla extract for about 2 minutes until light and fluffy. Scoop mixture into small discs and freeze until solid (1-2 hours).

In a saucepan, combine diced fresh strawberries and sugar over medium heat. Cook for about 45 minutes, mashing halfway for smoother consistency. Let jam thicken.

Mix dry ingredients together: whisk all-purpose flour, baking powder, baking soda, and salt in a large bowl. Set aside while preparing wet ingredients.

Beat softened unsalted butter and sugar until light and fluffy (about 3-4 minutes). Add egg and vanilla extract, mixing until pale and blended.

Gently fold dry ingredients into butter mixture until just combined. The dough should be soft and slightly sticky.

Divide cookie dough into quarters. Layer each with a spoonful of cooled strawberry jam and fold lightly to create swirls.

Preheat oven to 350°F (175°C). Flatten cookie dough in hand, place cheesecake disc in center, enclose with dough, and roll in sugar before placing on baking sheet.

Bake for 11-12 minutes until edges are golden. Cool on wire rack.

Gently press edges with a round cutter while warm for polished look. Allow to cool completely before serving.