Melt the chocolate in a pyrex measuring cup or glass bowl in the microwave for about 2 minutes at 50% power. Stir and if not completely melted, return to microwave for 30 more seconds and stir again. Repeat again if necessary but this should not take more than 3 minutes total time to melt.
Pour the chocolate into a medium bowl. Add the sugar, water and vanilla and whisk until smooth. A small electric hand mixer works well for this.
Beat in the egg until completely mixed.
Add the softened butter and beat until smooth.
This is enough frosting for 2 - 8 or 9-inch layers.