If you don't have white balsamic vinegar, substitute Champagne vinegar or apple cider vinegar.
Beat cream in a medium bowl at medium-high speed with an electric mixer until soft peaks form. Cover and chill until ready to use.
Whisk together egg yolks, honey, wine, and balsamic vinegar in top of a double boiler. Bring water in bottom pan to a light boil. Cook egg yolk mixture, whisking constantly, 8 to 10 minutes or until thick and foamy.
Remove from heat. Fill a large bowl with ice. Place top of double boiler containing egg yolk mixture in ice, and whisk 5 minutes or until completely cool. Remove from ice bath, and fold in whipped cream. If desired, cover and chill up to 24 hours. Spoon berries into bowls, and serve with custard.