Pour about 1 inch of water in a saucepan. Bring the water to a simmer and then turn the heat to low.
Place a metal bowl over the simmering water. Add the chocolate and heat until it has melted.
Meanwhile, bring about 1/4 cup of water to a boil.
Sift the confectioners’ sugar and then measure 1 1/2 cups.
With an electric mixer or whisk, beat about 1/2 cup of the confectioners’ sugar and 1 tablespoon of the boiling water into the melted chocolate. Repeat with another 1/2 cup of the confectioners’ sugar and another tablespoon of boiling water. Beat in the remaining 1/2 cup of sugar and 1 more tablespoon of water.
Add the corn syrup and vanilla and beat until smooth.
The mixture should be thick but pourable. If necessary, add more boiling water, about 1/4 to 1/2 teaspoon at a time, as needed.
Spoon the chocolate glaze evenly over the cake and spread gently.
Makes enough to ice a Bundt cake or cover an 8- or 9-inch one-layer cake.