Combine diced strawberries and 1/4 cup sugar in a medium saucepan and cook over medium heat for 45 minutes, mashing halfway through, until thickened and reduced to about 1/3 cup.

Mix softened cream cheese, 1/4 cup sugar, and 1/2 teaspoon vanilla extract until smooth. Divide into 18 equal portions, flatten each into a disc, and freeze until solid.

Beat softened butter and 1 cup sugar until light and fluffy. Add egg and 1 teaspoon vanilla extract and continue beating until pale and voluminous.

Whisk together flour, baking powder, and salt in a separate bowl. Gradually add to butter mixture and mix until just combined.

Divide dough into four parts in the mixing bowl. Layer 1/3 cup thick strawberry jam between flattened sections and fold dough gently to create jam pockets without fully blending.

Scoop dough into 18 two-tablespoon portions. Flatten each portion, place a frozen cheesecake disc on top, and wrap dough around the filling to encase it fully. Shape into slightly flattened discs.

Preheat oven to 350°F. Arrange cookies on baking sheets and bake for 11-12 minutes.

Allow cookies to cool on the baking tray for 10 minutes, then transfer to a wire rack to cool completely.