Preheat the broiler and line a medium baking sheet with aluminum foil.
Transfer the apricot halves to the prepared baking sheet and drizzle with the olive oil. Sprinkle with the sugar and some salt. Broil until the apricots are warmed through and the sugar is caramelized on top, 4 to 6 minutes.
Meanwhile, whip the cream, confectioners' sugar and vanilla in the bowl of a stand mixer fitted with a whisk attachment. Whisk on medium-high until the cream is fluffy and soft peaks form, about 2 minutes.
In a separate bowl, whisk the mascarpone by hand until soft and creamy. Fold in the whipped cream gradually until the two are combined.
Remove the apricots from the oven and transfer to a serving plate. Spoon 2 teaspoons of the whipped mascarpone into the cavity of each. Sprinkle with crushed pistachios and serve immediately.