Melt chocolate in a microwave according to package instructions. Set aside and let cool completely.
Combine sugar and water in a saucepan. Bring to a boil; let boil for 1 minute. Remove from heat and set aside.
Beat eggs in a large bowl using an electric mixer until frothy. Drizzle in sugar mixture slowly; beat on high speed until mixture turns pale yellow and expands in volume, about 5 minutes. Add butter by tablespoon one at a time with mixer running, beating well after each addition. Frosting will become watery; continue with remaining butter.
Mix in cooled melted chocolate. Beat on high speed until frosting thickens and becomes fluffy, about 5 minutes.
