In a bowl, stir together the flour, baking soda and salt.
Beat the cream cheese and butter together until light and fluffy. You can do this by hand but since this cookie dough was made with a stand mixer, the following are instructions for mixing the dough using a stand mixer. Choose the paddle attachment and beat on high for a minute.
Add the brown and white sugars to the cream cheese mixture. Over medium speed, mix until smooth.
Add the egg; mix until fully incorporated.
Set the speed to low. Add the flour mixture slowly. Scrape the bottom and sides of the bowl occasionally.
Dump the chopped Oreo cookies into the dough and fold in using a spatula.
Cover the bowl with cling film and chill the dough for at least two hours.
Preheat the oven to 350F.
Line a cookie pan with non-stick baking paper or a silicone mat.
Using a small ice cream scoop, scrape the chilled cookie dough and release on the prepared pan about two inches apart.
Bake for 18 to 20 minutes. The actual baking time depends on the size of the cookies AND how your oven performs. No two ovens are ever the same. As a guide, after 15 minutes, use a spatula to partially lift one cookie. If the bottom is lightly browned, it should be done. You can bake the cookies a little longer to allow the edges to brown but that is totally optional.
Cool the Oreo cream cheese cookies on the sheet for a few minutes to allow them to firm up a bit. Lift with a spatula and transfer directly to a wire rack. Sprinkle each cookie with a pinch of rock salt. Cool completely.
Store the Oreo cream cheese cookies in an airtight container at room temperature. BUT if you live in a region where the humidity goes above 90%, it is a better idea to refrigerate the cookies after 24 hours.