In a medium saucepan, combine the milk, cream, sugar, and pinch of salt over medium heat, stirring often to dissolve the sugar.
In a small bowl, beat the eggs.
Once the milk mixture is steaming, but not yet at a boil, slowly pour about 1/4 cup (60 milliliters) into the eggs while constantly whisking.
Once incorporated, slowly stream in and whisk another 1/2 cup (125 milliliters). Slowly pour the mixture back into the saucepan over medium-low heat while whisking. Cook while continuing to stir until just thickened enough to coat the back of a spoon, 170-180˚F (77˚C-82˚C). Be careful not to overcook or it will curdle.
Remove from heat and pour through a fine mesh strainer into a large bowl. Whisk in the olive oil until smooth.
Cover and refrigerate until well chilled, about 4 hours to overnight.
Transfer the chilled olive oil ice cream to an ice cream machine and churn according to manufacturer's instructions until thickened and creamy.
While the ice cream is churning, melt the chocolate in the microwave at 30 second intervals or in a double boiler on the stove until melted and smooth. Allow to cool slightly without hardening again.
During the last 5 minutes of churning, slowly drizzle all but two tablespoons of the chocolate into the ice cream maker in a small, thin stream. The amount of chocolate can be adjusted more or less to personal taste.
Once incorporated, transfer the churned ice cream to a freezer-safe bowl. Top with a drizzle of the remaining two tablespoons chocolate. Cover and freeze until firm, at least 4 hours.