Crush mint leaves in a small saucepan and add water; bring to a near boil, lower heat, and simmer for 10 minutes. Strain mint leaves from water and measure 3 tablespoons mint water. Reserve any remaining mint water for another use.
Mix white chocolate, 3 tablespoons mint water, and matcha on top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula until smooth, 5 to 10 minutes. Remove from heat and allow white chocolate mixture to cool to room temperature.
Beat cream in a bowl using an electric mixer until soft peaks form; fold into white chocolate mixture.
Whisk egg whites in a large bowl until soft peaks form; fold into white chocolate mixture using a rubber spatula. Divide mousse among 6 dessert cups and chill until set, at least 1 hour.