Drum roll, please! And the answer is
They used an fMRI scan (functional magnetic resonance imaging) during what is called an affect labeling task. So they had people do this task where they have to label someone's emotional expression (e.g. fearful or surprised). There are certain parts of the brain that are known to be involved in doing that task, particularly the prefrontal cortex modulating the emotional center which is the amygdala. When they did this study they found that the more mindful people were, the more activity in the frontal cortex quieting down the emotional center.
In other studies, mindfulness is shown to change brain activity and even structure with practice. For example, Sara Lazar's research found that the structure of parts of the brain differed in long-time meditators compared to non-meditators. There are now many studies supporting brain changes with various sorts of meditation, including mindfulness meditation.
PF: Are you speaking about neuroplasticity?
SS: Yes, the capacity of the brain to change as a function of experience. And as a geneticist, I'm really interested in epigenetic phenomenon, that is, the capacity of our genes to change in their expression as a function of experience. Meditation seems to do that as well! There is one really great study where a set of about 15 genes were shown to differ (in expression) as function of a type of meditation. Those genes are ones involved in the stress response. And I'm sure there will be more studies like that.
What's really cool about that, from my background in genetics, is that it illustrates that a mind state that we can self-induce can regulate gene expression - turn gene expression up or down.
There is a growing body of scientific evidence about mindfulness that I think is sufficient today to say: Try it, it's likely beneficial, harmless, free, and relatively simple.