Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper; this helps prevent sticking and makes cleanup a breeze.

In a small bowl, beat the softened cream cheese with the powdered sugar and 0.5 tsp of vanilla extract until smooth and creamy. Set aside.

In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.

In a large mixing bowl, using an electric mixer, cream together the softened butter, granulated sugar, and light brown sugar until light and fluffy, about 2-3 minutes. Beat in the large egg and the remaining 1 tsp of vanilla extract until well combined.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Don't overmix! Gently fold in the crushed Oreo cookies until evenly distributed throughout the dough.

Scoop rounded tablespoons of cookie dough onto the prepared baking sheets, leaving about 2 inches between them. Using your thumb or the back of a spoon, make a small indentation in the center of each cookie dough ball. Spoon about 0.5-1 tsp of the cheesecake filling into each indentation. Bake for 10-12 minutes, or until the edges are lightly golden and the centers are just set. The cheesecake might still look slightly soft.

Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. This helps them set up properly and prevents them from breaking.