Here is an interesting article on intermittent fasting and how it is good for the brain.
“Challenges to your brain, whether it’s intermittent fasting [or] vigorous exercise . . . is cognitive challenges. When this happens neuro-circuits are activated, levels of neurotrophic factors increase, that promotes the growth of neurons [and] the formation and strengthening of synapses. . . .”
The hormone which stimulates hunger is called Grehlin - "the hunger hormone" and it has been shown to be beneficial in PD:
Ghrelin is neuroprotective in Parkinson’s disease: molecular mechanisms of metabolic neuroprotection
"In Parkinson’s disease, ghrelin enhances dopaminergic survival via reduced microglial and caspase activation and improved mitochondrial function."