Crush cardamom pods with the flat bottom of a glass or a mortar and pestle; discard hulls. In a blender, whirl seeds until finely ground.
Add half the mango pulp, yogurt, and ice cubes to blender, along with 2 tablespoons sugar and 1/3 cup water; whirl until smooth. Add more sugar to taste and water to thin, if desired; whirl briefly to blend. Pour into a pitcher. Repeat with remaining mango, yogurt, and ice, 2 tablespoons sugar, and 1/3 cup water (plus more sugar to taste and water to thin, if desired); pour into the pitcher and stir to blend. Serve at once.