Mix mayonnaise in a bowl with remaining horseradish and season with lemon juice, salt, pepper and sugar.
Cut cornichon and beets into slices.
Thickly spread 4 slices of bread with thick horseradish mayonnaise mixture. Thinly spread remaining toast slices with remaining horseradish mayonnaise mixture.
Cover the thickly spread slices of toast with cornichon, beets and pastrami. Cover with the remaining slices of toast. Cut in half diagonally and serve on plates.