Combine cream cheese, sugar, and vanilla extract in a mixing bowl. Mix until smooth and creamy, about 2-3 minutes. Scoop into small discs and freeze on a parchment-lined baking sheet for at least 1 hour.

Dice strawberries and cook with sugar in a saucepan over medium heat for about 45 minutes, stirring occasionally until thickened. Let cool completely.

In one bowl, whisk flour, baking powder, baking soda, and salt. In another, beat butter and sugar until fluffy. Add egg and vanilla, mixing well. Gradually combine dry ingredients.

Gently fold in cooled strawberry jam into the dough, creating pockets of jam.

Preheat oven to 350°F. Flatten a portion of dough, place a cheesecake disc in center, wrap dough around it, and roll in sugar. Repeat for all dough and filling.

Bake cookies for 11-12 minutes, rotating halfway until edges are golden and centers are soft.

Let cookies cool on a baking sheet, press edges with a cookie cutter for shape, then transfer to a wire rack. Dust with powdered sugar before serving.