In a large bowl beat together the butter, brown sugar and white sugar until fluffy using an electric mixer.
Beat in the egg and vanilla extract until evenly mixed.
With the mixer on low speed beat in the flour, baking soda and salt.
Stir in the chocolate chips.
Cover the bowl and chill in the fridge for 30 minutes. You want the dough to feel slightly firm, but not hard.
To form the dough into balls, scoop about 1 - 1.5 tablespoon of dough and place an Oreo cookie on it horizontally. Place an additional 1 - 1.5 tablespoons of dough on top of the Oreo cookie. Making sure the Oreo is horizontal, press and pinch the cookie dough around the edges so that the entire Oreo is covered in chocolate chip cookie dough, forming a ball. I like to use a cookie scoop to scoop out the cookie dough.
Place the dough balls on a plate (keeping the Oreos horizontal) and repeat the process with the rest of the cookie dough. I got about 15 cookies in total. Cover the plate with plastic wrap and refrigerate for 3 hours, or overnight.
When ready to bake, preheat the oven to 350F degrees and line cookie sheets with parchment paper. Place the dough balls (keeping the cookies in the same orientation so that the Oreo stays horizontal) 3 inches apart on the lined cookie sheets.
Bake in the preheated oven for 12-15 minutes, or until the tops look just set.
Remove the trays from the oven, and optionally place a few extra chocolate chips on top of each cookie. Cool the cookies on the cookie sheet for at least 10 minutes, then transfer to a wire rack and continue cooling.
Notes
If you find the tops of the cookies aren't flattening down enough, simply press them down slightly before baking.
Cookie dough balls can be placed in a freezer bag and frozen for up to 2 months. Bake the dough from frozen as directed. They will take 1-2 minutes longer.
Store cookies in an airtight container at room temperature for up to 5 days.