Place Peeps in a medium sauce pan over medium-low heat with a 1/2 tablespoon of water.
Separate the Oreo cookie halves.
Scrape the filling into the pan with the Peeps.
Stirring occasionally, melt the Peeps. Make sure all the lumps are gone and the mixture is smooth.
Place half the Oreo cookies logo-side down onto a baking sheet that has been lined with parchment paper. This will make cleanup easier.
Remove the melted Peeps from the heat and let cool just enough so the mixture isn't runny.
Using a 1/2 tablespoon measure, scoop melted Peeps into the center of the cookies. Add just enough that the mixture gets near the cookie edge. If your mixture is too runny (hot) it might run over the sides. You'll get a feel for it after doing your first cookie or two.
Add the remaining cookie halves logo-side up on top of the Peeps-topped Oreos.
Let cool completely before serving. You can also stick them in the fridge for 15 minutes to set quicker.