Place white chocolate and 3 tablespoons heavy cream in the top of a double boiler. Add hot water to the bottom of the double boiler and place over medium-low heat. Stir occasionally until chocolate melts, 3 to 5 minutes.
Beat 3/4 cup heavy cream in a chilled glass or metal bowl with an electric mixer until soft peaks form.
Combine mango and sugar in a food processor; puree until smooth. Pour into a bowl; fold in melted white chocolate mixture and whipped cream.
Place hot water in a small bowl. Sprinkle gelatin on the water; allow it to melt 1 minute.
Pour softened gelatin into the mango mixture. Mix thoroughly with an electric mixer for 1 or 2 minutes. Transfer mixture to a 9-inch springform pan. Refrigerate until firm, 3 or 4 hours.