In a measuring cup, combine the half & half and milk. Pour 1/2 cup of that mixture into a separate bowl.
In the bowl with 1/2 cup of milk, whisk together the cornstarch, flour, and egg yolks. Set aside.
In a medium saucepan, stir the remaining milk mixture, sugar and salt together. Bring to a simmer over medium heat, stirring frequently. Make sure the milk does not boil.
Once all of the sugar is dissolved, whisk some of the hot milk mixture into the eggs to temper them. This will keep the yolks from scrambling when they are added to the hot saucepan.
Straining through a fine mesh sieve, pour the eggs into the simmering milk. Straining the mixture now will help prevent a lumpy pastry cream later.
Bring to a boil, while whisking vigorously to thicken the cream.
Remove from the heat and use a spatula to strain again through a fine mesh sieve.
Stir in the butter, vanilla, and peanut butter.
Cover the pastry cream tightly with plastic wrap to prevent a skin from forming. Allow the pastry cream to cool in the refrigerator. It will thicken as it cools.
While the pastry cream is cooling, get two small bowls and separate the Oreo cookie from it's cream center. Put the cookies in one bowl and the cream centers in another.
Transfer the cookies to a food processor and grind until they are fine crumbs. Reserve 1/4 cup of this mixture and put that on a plate. You will use this for the cream puff topping. Save the remaining cookie crumbs to add to the pastry cream.
Once the pastry cream is cooled, remove from the refrigerator.
Using a spatula, mix in the cookie crumbs to the pastry cream.
Transfer the prepared cream into a piping bag and pipe the cream into the puffs. You can tell when a puff has enough cream by its weight. Full puffs will be heavy.
Once the puffs are filled, microwave the cream centers for about 2 minutes, until they are smooth and sauce-like.
Dip each cream puff into the melted cream and then immediately roll the top in the reserved Oreo cookie crumbs.
Allow the topping to cool and serve immediately!