Melt 120g white chocolate in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each interval, 1 to 3 minutes.
Beat cream cheese and sugar together in a bowl using an electric mixer until creamy. Mix in the melted white chocolate, egg, green tea powder and vanilla extract until creamy. Pour onto the digestive biscuit base.
Bake in the preheated oven until centre jiggles evenly when cheesecake is lightly shaken, about 25 minutes. Let cheesecake cool, about 30 minutes.
Bring cream to the boil in a saucepan. Stir in 60g white chocolate until smooth. Stir in syrup and water, in that order. Pour glaze on top of the cheesecake; tilt and rotate so glaze coats top evenly. Let rest until glaze is set, at least 15 minutes. Refrigerate until chilled, about 1 hour.