Measure 2 1/2 cups nonfat milk. Pour 1/2 cup into a small bowl and set aside for dipping; use the remaining 2 cups for the pudding.

In a medium bowl, whisk the 13.4 ounce box instant vanilla pudding mix with the 2 cups nonfat milk until smooth. Let the pudding sit about 5 minutes to thicken.

Set an 8×8-inch pan on the counter. Remove 4 Oreos from the bag and set them aside to crush later; the remaining 32 Oreos will be used for the layers.

Working with 16 Oreos at a time, dip each Oreo briefly into the reserved 1/2 cup milk (do not soak) and arrange them in a single layer on the bottom of the 8×8-inch pan.

Spread half of the thickened pudding evenly over the first Oreo layer.

Spread half of the 18 ounce container of whipped topping evenly over the pudding.

Dip the next 16 Oreos, one at a time, in the reserved milk and arrange them in a single layer over the whipped topping.

Spread the remaining pudding evenly over the second Oreo layer.

Spread the remaining whipped topping evenly over the pudding.

Place the 4 reserved Oreos in a sealed plastic bag and crush them with a rolling pin or chop them finely with a knife. Sprinkle the crumbs over the top of the whipped topping.

Cover the pan tightly and chill in the refrigerator at least 4 hours before serving (overnight is best).

Store leftovers in the refrigerator for up to 3 days.