Combine the diced mango, lime juice, and 2 tablespoons of granulated sugar in a blender or food processor. Blend until completely smooth. Set aside or refrigerate until ready to use.

In a small saucepan, combine the passionfruit pulp (with seeds) and 1/4 cup granulated sugar. Bring to a gentle simmer over medium-low heat, stirring until the sugar dissolves. Continue to simmer for 3-5 minutes, stirring occasionally, until the mixture slightly thickens. It should still be pourable but less watery. Remove from heat and let cool completely. Once cool, strain through a fine-mesh sieve to remove most of the seeds, pressing on the solids to extract all liquid. Discard seeds. Set the smooth passionfruit syrup aside.

In a large saucepan, combine the heavy cream, whole milk, and a pinch of salt. Heat over medium heat until the mixture just begins to simmer around the edges, but do not boil. Remove from heat.

In a separate medium bowl, whisk the 3/4 cup granulated sugar and egg yolks until light yellow and creamy.

Slowly temper the egg yolks: gradually pour about 1 cup of the hot cream mixture into the egg yolk mixture, whisking constantly to prevent the eggs from scrambling. Once combined, pour the tempered egg mixture back into the saucepan with the remaining hot cream.

Return the saucepan to medium-low heat. Cook, stirring constantly with a wooden spoon or whisk, until the custard thickens enough to coat the back of the spoon (reaching about 175-180°F or 80-82°C). Do not boil. This usually takes 8-10 minutes.

Remove the custard from heat and stir in the vanilla extract. Pour the custard through a fine-mesh sieve into a clean bowl to remove any potential bits of cooked egg. This will ensure a smooth ice cream.

Cover the surface of the custard with plastic wrap (to prevent a skin from forming) and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.

Once the custard is thoroughly chilled, churn it in your ice cream maker according to the manufacturer's instructions. This usually takes 20-25 minutes, until it reaches the consistency of soft-serve ice cream.

During the last 5 minutes of churning, gradually add the prepared mango puree to the ice cream maker. Continue to churn until just combined.

Transfer half of the churned mango ice cream to a freezer-safe container. Drizzle about half of the passionfruit syrup over the ice cream. Add the remaining mango ice cream and drizzle with the rest of the passionfruit syrup. Using a knife or spoon, gently swirl the passionfruit syrup through the ice cream a few times, being careful not to overmix.

Cover the container tightly and freeze for at least 4-6 hours, or until firm, before serving.