Dissolve gelatin in 4 tablespoons hot water in a bowl. Set aside.

Mix brown sugar and egg yolks together in a medium bowl. Set aside.

Heat milk in a saucepan over low heat, about 5 minutes. Stir in gelatin mixture until dissolved, making sure not to overheat milk. Remove from heat. Pour milk mixture into egg mixture gradually, stirring well.

Mix 2 tablespoons hot water and green tea powder together in a bowl. Set the bowl of gelatin mixture on top of a bowl filled with ice water; stir matcha paste into mixture as it cools.

Whip heavy cream in a bowl using an electric mixer until firm but not yet forming peaks, about 3 minutes. Add to matcha mixture; stir well until fully incorporated, about 1 minute.