Saute the onion at a medium heat for 5 minutes. Once slightly browned, add balsamic and sugar and saute for 2 minutes until the liquid has reduced to a syrupy consistency. Melt the butter over a medium heat in a second pan and add the mushrooms. Saute for 2-3 minutes or until the mushrooms are slightly cooked and butter has browned. Stir in the seasonings and cream and reduce down to a thick sauce. Whisk the eggs in with butter and cream. Into a third pan add some oil just to coat the pan. Pour the eggs in and scramble trying to move the egg as little as possible.
To Assemble: Spread the cream cheese over the toasted rye bread then spoon on 1tbsp onions then the eggs and the mushrooms. Garnish with chives and parmesan.