Remove the peel from the carrot and celery or parsley root and cut into thin slices. From the zucchetti use only the peel with a little meat. Remove the seeds from the peppers. Cut all these prepared vegetables into narrow strips and these into small cubes.
Blanch the vegetable cubes in a little salted water for just two to three minutes. Drain and set aside, covered with plastic wrap, until ready to use.
In a medium frying pan, melt the butter. Add the flour and cook, stirring, until softened, just over a minute. Slowly pour in the soup. Bring to a boil and reduce heat to low for five minutes.
Add the egg yolk and the cream, stir well and season with salt and pepper. Up to this point the soup can be prepared.
Immediately before serving, bring the soup to a boil. Reduce the temperature to the lowest setting. Add the egg yolk-cream mixture, stirring vigorously, seasoning the soup if necessary.
Then add the champagne and heat the soup again very briefly, whisking vigorously. Serve immediately in heated cups or plates and sprinkle with the vegetable confetti.