In a medium bowl, whisk together the egg yolks and first 125g sugar for 1 minute and set aside.
In a medium side pot, combine the second 125g sugar, whipping cream, and milk and bring to a boil. Ladle half the hot cream mixture over the egg mixture and whisk. Pour everything back into the pot and whisk over medium-low heat, continually stirring to avoid curdling the mixture.
Cook until the mixture coats the back of a spoon, about 5-10 minutes.
Take a large sized bowl and fill it with ice and cold water. Place a medium sized bowl inside the ice bath, and pour the mixture into the medium bowl.
Whisk in olive-oil and chill overnight.
Place mixture in the ice cream machine and churn according to the machine's directions, about 10-15 minutes.
This recipe uses Frescolio's Basil Infused EVOO. You could also try any of the following EVOOs for a different taste: