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In a medium saucepan, cover the beets with water and bring to a boil. Simmer over moderate heat until tender, about 45 minutes. Peel the beets and cut them into 1-inch-by-1/4-inch strips.
Meanwhile, in a small bowl, toss the cucumber with the salt and sugar and let stand for 10 minutes. Squeeze out the excess moisture.
In a large bowl, toss the beets with the herring, mayonnaise and onion. Spoon 2 rounded teaspoons of the herring salad onto Chinese soup spoons. Garnish with a few cucumber sticks and a dollop of wasabi paste and serve.