Make the ice cream: In a medium bowl, whisk together the sweetened condensed milk, olive oil, and salt until smooth and fully combined.
In a separate large bowl (or the bowl of a stand mixer), whip the heavy cream with a hand mixer or stand mixer until stiff peaks form. The cream should hold its shape firmly when the whisk is lifted.
Scoop a small spoonful of the whipped cream into the condensed milk mixture and stir it in briskly to loosen it.
Pour the lightened condensed milk mixture into the bowl of whipped cream. Using a spatula or large spoon, gently fold everything together, sweeping from the bottom and sides of the bowl until fully incorporated while keeping as much air in the mixture as possible.
Transfer to an airtight container and freeze until set, at least 3 hours or preferably overnight.
Make the hot fudge: In a small microwave-safe bowl, combine the sweetened condensed milk, chopped chocolate, and salt. Heat in short 30-second bursts, stirring between each, until the chocolate is fully melted and the mixture is smooth (about 30-60 seconds total). Drizzle in the olive oil, stirring until glossy and fully emulsified.
Alternatively, warm the condensed milk, chocolate, and salt in a small saucepan over medium heat, stirring frequently until melted and smooth. Remove from the heat and mix in the olive oil.
To serve: Let the ice cream sit at room temperature for about 10 minutes before scooping. Spoon over the warm or room-temperature hot fudge.
The hot fudge can be stored in an airtight container in the fridge for up to 5 days. Reheat briefly in the microwave until pourable. The ice cream keeps well in the freezer for up to 1 month.