Preheat the oven and grease a 9x13-inch baking pan. Prepare and bake the white cake mix in the pan according to the package directions (usually about 30 minutes at 350°F), until a toothpick in the center comes out clean. Let the cake cool for 15 minutes.

Using the round handle of a wooden spoon, poke holes all over the warm cake about 1 inch apart, pushing most of the way down without touching the bottom of the pan.

In a medium bowl, whisk the pudding mix with 1 ½ cups milk for 1 minute. Immediately pour the pudding evenly over the cake (or squeeze it into the holes with a squeeze bottle), nudging it toward the holes with a spatula. Refrigerate until the cake is completely cool, about 30 minutes.

In a large bowl, beat the softened cream cheese and powdered sugar with a hand mixer until smooth. Add the 2 tablespoons milk and beat until creamy.

Finely crush 6 Oreo cookies and stir them into the cream cheese mixture. Spread it evenly over the cooled cake with an offset spatula, all the way to the edges.

Spread the whipped topping over the cream cheese layer. Roughly crush the remaining 12 Oreo cookies and sprinkle them over the top.

Cover and refrigerate for at least 4 hours, or overnight, before slicing and serving cold.