In a small bowl, blend the softened cream cheese, sour cream, and sugar until smooth. Measure the mixture by the tablespoon, placing each portion on a parchment-lined baking sheet to freeze.

In a large mixing bowl, cream the butter and brown sugar until the mixture is light and fluffy, approximately 5–7 minutes. Add the eggs and vanilla, blending thoroughly. In a separate bowl, sift together the flour, salt, baking soda, and baking powder, then gradually incorporate this into the creamed mixture. Gently fold in the Oreo pieces. Using a quarter-cup measurement, portion the dough onto a parchment-lined baking sheet and refrigerate for about one hour.

Flatten each chilled dough ball into a disk, place one frozen cheesecake filling portion in the center, and wrap the dough around it to completely encase the filling. Place the filled dough balls back in the refrigerator to chill for an additional hour.

Preheat the oven to 350°F. Arrange the dough balls on parchment-lined baking sheets, spacing them about 4 inches apart.

Bake for 15–20 minutes or until the edges and tops are golden brown. Allow the cookies to cool on the baking sheet for five minutes, then transfer them to a wire rack to finish cooling. Store in the refrigerator for optimal freshness.