Separate the eggs and retain only the yolks.
In a mixing bowl, whisk the egg yolks with sugar until smooth and fluffy. Add the vanilla extract to the egg yolk mixture and continue whisking until well combined.
In a medium saucepan, combine the whole milk and heavy cream. Heat the mixture over medium-low heat, stirring constantly, until it is just about to boil. Do not let it boil.
Temper the egg yolk mixture by gradually adding a small amount of the warm milk and cream mixture into the eggs while whisking continuously.
Once tempered, pour the egg yolk mixture back into the saucepan with the remaining milk and cream mixture.
Cook the mixture over low heat, stirring constantly, until it thickens and coats the back of a spoon or silicon spatula. This should reach approximately 160°F.
Remove the saucepan from heat and pour the custard mixture into a large airtight container. Stir in the olive oil and sea salt, ensuring they are evenly incorporated into the custard base. Cover the container and refrigerate the custard base until completely chilled, preferably overnight.
Once chilled, churn the custard base in an ice cream machine according to the manufacturer's instructions until it reaches a soft-serve consistency. Transfer the churned ice cream into a closable container or cover with parchment paper.
Place the container in the freezer for at least a couple of hours to allow the flavors to fully develop and to achieve the perfect ice cream consistency.
When serving, drizzle high-quality olive oil over the ice cream and sprinkle with a pinch of sea salt for an elegant finishing touch.