Make the ice cream base. Heat the heavy cream and half-and-half in a saucepan over medium heat until it reaches a simmer and forms a skin on the surface.
Off the heat, whisk in 1/2 cup sugar, the salt, and the vanilla, whisking until the sugar is fully incorporated.
Let the base come to room temperature, then refrigerate until cold (it can be made up to 3 days in advance).
Just before you’re ready to make the ice cream, hull the strawberries and cut them into 1/2-inch dice.
Add them to a bowl with the rest of the berries and the remaining 1/4 cup sugar.
Toss well, then use a potato masher or pestle to mash the fruit just a bit.
Fold in the olive oil and set aside.
Give the ice cream base a quick whisk, pour into your ice cream maker, and turn on the machine.
Once the ice cream holds its shape, add in the berries with all their juices and finish churning.
You can enjoy the ice cream as a soft serve after churning or, for a firmer consistency, transfer to a freezer-safe container and place in the freezer for 2 hours or more.
Before serving, garnish portions with more berries if desired.