In a large saucepan, combine the 2 cups sugar, the water, and corn syrup. Do not stir. Cook over medium-high heat, swirling pan often, for 12 to 15 minutes or until syrup is dark amber in color. Remove from heat. Very carefully whisk in the 1/2 cup cream, 1/2 cup butter, and the 1/2 teaspoon vanilla. (The mixture will sputter and pop!) Continue whisking until perfectly smooth. Pour immediately into tart shell. Allow to stand about 1 hour or until caramel is set, but not firm.
Place chocolate in a medium bowl. In a small saucepan, bring the 3/4 cup cream to boiling. Pour immediately over chocolate (do not stir). Allow to stand for 5 minutes, then whisk until perfectly smooth. Carefully pour warm ganache topping over tart. Cover loosely; chill overnight.