Bring salted water to a boil. Add polenta, stirring continuously over low heat. Cook slowly for about an hour. Keep stirring so that the polenta does not burn. Finally, mix in the cream and Parmesan cheese. Cool.
Place about four heaped tablespoons of polenta between two sheets of household foil, press to level at about 3 mm. Remove top foil. Place a piece of fresh goat cheese in the center. Wrap the cheese all around with the polenta, forming it into a kind of hamburger in the foil. Turn first in the beaten eggs, then in the chopped nuts on the other side. Toast in olive oil on both sides until golden brown.
Cut raw vegetables into small pieces, drizzle with olive oil and balsamic vinegar, and season with salt and freshly ground pepper to taste. Arrange the vegetables on a plate. Form the sliced polenta burger in the middle. Decorate with cherry tomatoes.