Combine the milk, sugar, and salt in a medium saucepan and warm over medium heat until it is steaming. Do not boil. While the milk is warming, pour the cream into a large bowl and set a strainer over the top.
In a separate bowl, whisk together the egg yolks. Slowly pour the warm milk mixture into the egg yolks, whisking constantly. Pour the egg mixture back into the saucepan, scraping all of the mixture into the pan.
Stirring constantly with a heatproof spatula, warm the egg mixture over medium heat, scraping the bottom of the pan as you stir. When the mixture has thickened and coats the spatula, pour the custard through the strainer into the heavy cream.
Stir to combine the custard with the cream, and then add the olive oil. Whisk vigorously until well blended, then stir until cool over an ice bath. Pour the mixture into your ice cream maker and process according to the manufacturer's instructions.
Serve immediately for soft-serve ice cream or transfer to an airtight container and freeze until ready to serve.