Combine mango pulp, sugar, and water in a medium saucepan over medium heat. Stir constantly until the sugar dissolves completely, about 2-3 minutes. Don't let it boil—you're just warming it enough to dissolve the sugar. Remove from heat immediately once you see the mixture smooth out.
Pour the warm mixture into a blender or food processor. Add lime juice, lemon juice, salt, orange blossom water, and cardamom. Blend until completely smooth and combined, about 1 minute. Taste and adjust the citrus if needed—you want brightness but not pucker.
Strain the mixture through a fine-mesh strainer into a large bowl. Press gently with the back of a spoon to get all the liquid through. This step removes any fiber and creates that silky-smooth texture you're after. Don't rush it or you'll have grainy sorbet.
Let the mixture cool to room temperature, about 15 minutes. Then refrigerate for at least 1 hour (or up to overnight). Cold mixture churns better and freezes more evenly—honestly, this timing makes a huge difference in your final texture.
Pour the chilled mixture into your ice cream maker and churn according to manufacturer instructions. Most machines need 20-25 minutes. You'll see it go from liquid to soft-serve consistency—stop when it looks like soft serve ice cream.
Transfer the churned fresh mango sorbet summer to a freezer-safe container. Smooth the top and cover tightly with plastic wrap or parchment paper (this prevents ice crystals). Freeze for at least 2 hours before serving—overnight is even better.
Scoop into chilled bowls and top with fresh mint and crushed pistachios. Let it sit at room temperature for 2-3 minutes if it's too hard to scoop easily. Serve immediately and watch everyone's faces light up.