Mix mango with 2 teaspoons sugar. Let macerate for 30 minutes. Place white chocolate in a metal bowl set over a saucepan of simmering water and stir until melted. Remove from heat and whisk until smooth. Let cool slightly. Gradually whisk in yogurt. Divide mixture between 2 small bowls.
Whisk remaining 2 teaspoons sugar and matcha powder in another small bowl. Add 1 tablespoon hot water; whisk to form a thick paste. Add paste to 1 bowl with white chocolate-yogurt mixture; whisk to blend well.
Divide mango among 4 Old Fashioned glasses. Make a well in green yogurt mixture and pour white yogurt mixture into center. Fold once or twice, just enough to create swirls. Spoon over mango, dividing equally.
