I actually made two attempts. The very first was with storebought dough and I tried completely encasing the Oreo with it. Unfortunately, the normal cookie dough is so fluid at baking temperatures, before it starts to set, that I ended up with chocolate chip saucers with an Oreo island in the middle. Fortunately, short of burning the cookies entirely, it's still delicious.
My second time, I thought I'd leave the cookie dough as thick dollops above and below the Oreo, so as it settled during baking, it would, I hoped, just encase the Oreo.
Nope. Close, but no cigar.
Obviously the storebought dough just isn't firm enough. I'd have to do something like try making it by hand. Adding extra flour might work, or substituting a fraction of AP flour for something with higher gluten like bread flour, but since I knew someone has already figured all these details out to have posted this idea online in the first place, I thought I'd see what they had to suggest.
The original recipe apparently comes from here.
After all that hassle, I came up with a workable, if inelegant, compromise: muffin tins.
I overdid it, but it worked: two cookie dough squares in the bottom of each depression of the muffin tin, then the Oreo, then two more squares. It was almost too much cookie, but it held together and baked up just fine.
I tried it again using a mini muffin tin and one square each on top and bottom (and mini Reese's peanut butter cups--I thought they'd melt and fall apart without the support of the tin--but let's not get distracted), but that didn't turn out as well. The top squares spread out during baking and all touched, so I couldn't twist them out one at a time like I could with the regular size muffin tin. They did bake up fine and were delicious, but I had a lot of cookie shrapnel piled up by the time I got all the cookies extracted. But that's an adventure for a later time.
After all that hassle, I came up with a workable, if inelegant, compromise: muffin tins.
I overdid it, but it worked: two cookie dough squares in the bottom of each depression of the muffin tin, then the Oreo, then two more squares. It was almost too much cookie, but it held together and baked up just fine.
Big hit with my coworkers, even the diabetic one. I just wish I'd made more to share.