How to Make It
Melt 2 tablespoons of the butter in a large skillet. Add the livers and cook over moderately high heat, stirring occasionally, until barely pink in the center, about 7 minutes. Transfer the livers to a medium bowl and let cool completely, then chop coarsely.
Meanwhile, melt the remaining 2 tablespoons of butter in the skillet. Add the onions and cook over moderately low heat, stirring occasionally, until browned, about 12 minutes. Let the onions cool completely.
Add the onions, eggs, Cognac, port, salt and white pepper to the chicken livers and stir to combine. Cover and refrigerate overnight.
In a medium bowl, combine the white vinegar with the shredded beet and add horseradish to taste. Cover and refrigerate the beet overnight.
To serve, spread each toast with 1 tablespoon of the chopped liver and sprinkle with a pinch of the beet. Arrange on a platter and serve.