Tie the parsley, bay leaves and rosemary together with kitchen twine. Add the herb bundle to the diced onions and cook over low heat, stirring a few times, until fragrant, about 3 minutes. Sprinkle the sugar over the onions and cook, without stirring, until the sugar melts, about 5 minutes. Increase the heat to high and cook, without stirring, until an amber-brown caramel forms, about 6 minutes. Stir in the white balsamic vinegar and simmer over low heat, stirring a few times, until the jam is thick, about 5 minutes. Discard the herb bundle. Season the jam with salt and let cool to warm.