This 2015 published random clinical trial (the gold standard in research) is an exciting study.  It evaluated 447 healthy participants and assigned them to 3 distinct diet patterns.  After following the participants for five years, the authors concluded that a Mediterranean diet supplemented with olive oil (1 liter/week) or nuts was associated with improved measures of cognitive function in an older population.

Objective:

To investigate whether a Mediterranean diet supplemented with antioxidant-rich foods influences cognitive function compared with a control diet.

Conclusions and Relevance:

In an older population, a Mediterranean diet supplemented with olive oil or nuts was associated with improved composite measures of cognitive function.

JAMA Intern Med. 2015;175(7):1094-1103. doi:10.1001/jamainternmed.2015.1668

https://jamanetwork.com/journals/jamainternalmedicine/fullarticle/2293082