In a nonstick saucepan, over medium heat, combine the milk, sugar, and vanilla. Whisk to dissolve the sugar. When the mixture comes to a gentle boil, take 1 cup of the milk-sugar mixture and add it to the yolks. Whisk to blend well. Temper the egg mixture to the milk mixture. Cook over medium heat until it thickens slightly, 4 to 5 minutes, whisking occasionally. Dissolve the cornstarch in the water. Over medium heat, slowly add this mixture to the saucepan, whisking constantly for 1 minute. Using a wooden spoon, continue stirring for about 2 minutes. Stir in the coconut. Add the butter and stir until it is completely melted and mixture has thickened to a custard, about 2 minutes. Soften the gelatin in the water and stir into the hot custard. Pour the mixture into a glass bowl. Cover with plastic wrap, pressing the wrap down the surface of the custard to prevent a skin from forming. Cool completely, stirring occasionally and chill for at least 4 hours. In a mixing bowl, combine the crumbs and butter. Mix well. Press into the bottom of a 10 inch spring-form pan. Bake until firm, about 6 to 8 minutes. Remove and cool completely. Fold in 2 cups of the whipped cream to the pastry cream. To assemble, spread about 1 cup of the custard on the bottom of the crust. Arrange about a third of the banana slices, crowding them close together, over the custard. Next, spread 1 cup of the custard over the bananas. Arrange another third of the banana slices close together over the custard. Top with 1 cup of the custard and the banana slices. Top with the remaining custard, covering the bananas completely to prevent them from turning brown. Cover with plastic wrap and chill for at least 4 hours. Remove from the refrigerator and top with the remaining whipped cream. Remove the spring-form and press the ladyfingers firmly into the sides on the pastry cream.
Slice the dessert into individual servings and garnish with fresh mint sprigs.