In a large mixing bowl, beat the softened butter until smooth and creamy.
Add the brown sugar. Beat until the mixture is light and well combined.
In a separate bowl, whisk together curd and vanilla extract until smooth and creamy.
Add the curd mixture to the butter mixture and whisk until fully incorporated.
Gradually add the all-purpose flour, cornstarch, baking soda, and salt to the wet mixture.
Stir gently with a rubber spatula until a soft cookie dough forms and no dry flour remains. Avoid overmixing to keep the cookies tender.
Fold the crushed Oreo cookies into the dough until evenly distributed.
In another bowl, mix the cream cheese and powdered sugar, until smooth to prepare the cheesecake filling.
Cover the cookie dough and refrigerate for 30 minutes. Chilling helps the dough become easier to handle and prevents excessive spreading during baking.
Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Scoop portions of chilled dough and flatten each portion slightly. Place a small amount of cheesecake filling in the center and gently seal the dough around it.
Arrange the filled cookie dough balls on the prepared baking sheet, leaving enough space between each cookie for spreading.
Bake for 10 to 12 minutes, or until the edges are lightly golden and the centers are set.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire cooling rack.
Once cooled, add a small amount of extra cheesecake filling on top and sprinkle with crushed Oreo pieces before serving.