The distinctive tart-sweet flavor of passion fruit makes a refreshing dessert or intermezzo. Serve it over diced mango and papaya for a tropical fruit salad.
Look for passion fruits that feel heavy for their size (they'll yield more juice). There are two common varieties: the purple subtropical type grown in California, Florida, and New Zealand; and the yellow tropical fruit grown in Hawaii. Either variety will work in this recipe, although the purple fruit has sweeter juice and a stronger flavor and perfume. It's essential to let passion fruits ripen at room temperature until their hard skin is dented and wrinkled, as this sweetens the pulp.
Make a simple syrup by combining the sugar and water in a small pan and bringing to a boil over high heat. Stir to dissolve the sugar, then remove from the heat.
Add the passion fruit pulp and salt to the sugar syrup and cool to room temperature. Refrigerate, covered, until completely cold. At this stage the mixture can be stored up to 2 days.
Strain the syrup through a fine mesh sieve set over a bowl. Press hard to extract all the liquid; discard the seeds and pulp.
Stir in the lime juice and rum. Transfer to an ice cream maker and process according to the manufacturer's instructions. Freeze until firm.