Can we stop the brain from processing a particular task?
One answer is through turning off these messages or "tasks" via mindful awareness and focused attention on another task requiring much less cognitive load - like breathing. 

Look up Dr. Jeffery Schwartz's book "You Are Not Your Brain" for scientific data on this.

Basically, latest scientific research shows that we can use our mind to stop the brain (or really work around the task, observing it, until it slowly diminishes activity in the bran).

It's the old saying; "mind over matter" - where the brain is also matter.