What part of the brain is involved in planning and impulse control?

Frontal lobe. Recent studies, and the case of phineas gage in 1848, show frontal lobe is important in controlling overall impulsivity. But, patients with temporal lobe epilepsy can also be impulsive. Overall chemical levels, such as testosterone and serotonin, can also be linked to mood disturbances with impulsive component. Lastly, genetics also plays a factor. Still many unknowns.
Frontal. The frontal lobe embodies learned and complex social inhibitions. When it is damaged, primitive reactions can be "dis inhibited" as in alzheimer's -- or intoxication.
Complex answer. The brain is a complex organ that depends on many working parts. The temporal lobe is important in memory while the parietal lobe is important in putting information together and planning out an action. Fiber tracts connect the various lobes of the brain to make it work.