In a small saucepan over medium heat, combine the chopped strawberries and sugar. Stir until the strawberries release their juices and soften, about 5 minutes.

Add the cornstarch mixture and lemon juice, cooking for an additional 2-3 minutes until the sauce thickens. Remove from heat and let it cool completely.

Optionally, puree the sauce for a smooth texture or keep it chunky for more texture in the cookies.

In a mixing bowl, beat the softened cream cheese, sugar, and vanilla extract until smooth and creamy.

Drop teaspoon-sized portions onto a parchment-lined tray and freeze for at least 30 minutes.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.

In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.

Incorporate the egg, egg yolk, and vanilla extract, mixing until well combined.

Gradually add the dry ingredients to the wet mixture, stirring just until combined to avoid overmixing.

Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.

Scoop a tablespoon of cookie dough, flatten it slightly, and place a frozen cheesecake ball in the center.

Cover it with another tablespoon of dough, sealing the edges well before gently flattening the dough ball.

Drizzle about 1/2 teaspoon of the cooled strawberry sauce atop each cookie, swirling it gently with a toothpick for a marbled effect.

Bake the cookies for 11-13 minutes until the edges are lightly golden and the centers look slightly soft.

Allow to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.