To make simple syrup: Dissolve sugar and water over medium heat. Chill well.
Blanch basil leaves in boiling water for 10 seconds. Plunge into ice water and drain. Puree in blender with chilled simple syrup. Allow to steep 1 hour. Strain through cheese c
To make caramel: In a heavy 10-inch skillet cook 1/2 cup sugar and 3 tablespoons water over moderately high heat until it is a golden caramel. Whisk in 3 tablespoons of butter, one by one into the caramel and and then arrange thick 1/3-inch mango slices over caramel and butter mixture
Roll puff pastry out to 1/8-inch thickness. Cut pastry 1/2-inch larger than skillet.
Place puff pastry over mangoes. Bake in a 425 degree oven (375 convection) for approximately 20 minutes until pastry is puffed and golden brown. Allow to rest 5 minutes. Invert onto serving dish and serve with ice cream and basil syrup.