Add the milk, heavy cream, vanilla bean seeds and vanilla bean to a heavy-bottomed saucepan. Set over medium heat and bring to a very low simmer. Keep an eye on it and stir often while you prepare the egg yolks.
Meanwhile, add the yolks, sugar and salt to a large bowl and whisk until light and fluffy, about 3 minutes. Whisk in the olive oil and beat vigorously for another minute or so until it's completely emulsified.
Slowly ladle in about 1 cup of the hot milk mixture into the eggs and olive oil, whisking the whole time. This is called tempering - it's getting the yolks used to the hot temperature of the milk and preventing them from scrambling. Add the tempered eggs back into the milk in the saucepan and stir until it thickens just slightly and coats the back of a spoon. This should take about 5 minutes.
Strain the custard through a fine mesh strainer into an 8-cup measuring cup. Let cool, and then cover with plastic wrap and place in the fridge. You want the mixture to cool down completely and be well chilled before you run it in your ice cream machine. You can make this the night before.
Freeze the ice cream according to manufacturer's instructions - you should let it run about 30 minutes - until it looks like soft serve. Then place the ice cream back into the freezer until firm, another hour. Keep in mind that gelato is softer than ice cream.