Preheat the oven to 325 degrees. Butter a 9-inch square baking dish for thicker bars, or a 9×13 baking dish for thinner bars.
Cream the butter, brown sugar, white sugar, peanut butter, and vanilla. Add the eggs one at a time, beating until well mixed.
Add the flour and baking powder and mix for less than 1 minute with an electric mixer or stir with a wooden spoon until all flour is incorporated (batter gets tough to work with if you mix it for too long). Add the cream and use electric mixers or wooden spoon to stir until incorporated. Batter should be thick but spreadable.
Spread half the batter in the prepared dish; layer Oreos evenly over the batter; top with remaining half of batter. Bake for 40-50 minutes, depending on the size of your pan (less time for a rectangle, more time for a square) and whether or not you like them to still be a little soft and doughy. I baked mine for 40 minutes or until the edges were browning and the middle was just a little soft.