Whisk cornstarch with 3 tbsp cold milk until smooth.
Heat remaining milk, cream, sugar, and salt over medium heat until steaming; whisk in the slurry.
Cook, stirring constantly, until thick enough to coat a spoon, 3–5 minutes after it bubbles; avoid a violent boil.
Off heat, whisk in chilled mango puree and vanilla or cardamom. Strain if lumpy.
Cool in an ice bath, then refrigerate until very cold, at least 4 hours or overnight.
Churn per ice cream maker instructions until soft-serve consistency.
Transfer to a chilled container, press plastic wrap to the surface, and freeze 3–4 hours for firm scoops.