Crack cardamom pods by gently pressing with a rolling pin. Combine with 4 cups milk in a 3- to 4-quart pan; stir occasionally over medium-high heat until milk is boiling, 9 to 15 minutes.
Meanwhile, in a small bowl, mix 1/4 cup sugar, the cornstarch, and the ground cardamom. Stir in remaining 1/4 cup milk. When milk in pan is boiling, remove from heat and gradually whisk in cornstarch mixture. Return to medium-low heat and stir just until mixture comes to a boil, 3 to 7 minutes. Pour through a fine strainer set over a bowl; discard residue. Ladle pudding into 6 to 8 small bowls or ramekins (3/4- to 1-cup capacity). Let cool about 10 minutes, then cover and chill until cold and set, at least 1 1/2 hours.
Pit and peel mango. Cut flesh into about 1-inch chunks (you need 2 cups). In a food processor or blender, combine 2 cups mango, remaining 1/4 cup sugar, and ginger liqueur if using; whirl just until mango is coarsely puréed (mixture should be slightly chunky). Cover and chill.
Just before serving, spoon all of the mango mixture evenly over puddings. Garnish with mint leaves.