Preheat oven to 350°F. Butter 10-inch-diameter springform pan. Line bottom of pan with parchment round; butter parchment. Wrap 3 layers of heavy-duty foil around outside of pan, bringing foil to top of rim.
Combine 1 cup water and sugar in small saucepan. Bring to boil over medium heat, stirring until sugar dissolves. Simmer 5 minutes.
Remove from heat.
Melt butter in large saucepan over low heat.
Add chocolate and whisk until smooth.
Whisk sugar syrup into chocolate; cool slightly.
Add eggs to chocolate mixture and whisk until well blended.
Pour batter into prepared pan.
Place cake pan in large roasting pan.
Add enough hot water to roasting pan to come halfway up sides of cake pan.
Bake cake until center no longer moves when pan is gently shaken, about 50 minutes.
Remove from water bath; transfer to rack. Cool completely in pan.
Bring whipping cream to simmer in small saucepan over medium heat.
Remove from heat.
Add chocolate and whisk until smooth.
Pour over top of cake still in pan. Gently shake pan to distribute ganache evenly over top of cake. Refrigerate cake in pan until ganache is set, about 2 hours. DO AHEAD: Can be made 2 days ahead. Cover and keep refrigerated.
Run knife around pan sides to loosen cake; release sides.
Cut cake into wedges and serve with whipped cream.
