To make the sauce: In the top of a double boiler, whisk together yogurt, lemon juice, egg yolks, mustard, salt, sugar, pepper, and hot sauce. Cook over simmering water, stirring constantly, 6 to 8 minutes, or until sauce is thick enough to coat the back of the spoon.

In a large stock pot, heat 2 quarts of salted water to a boil. Carefully break eggs one at a time into boiling water. When all eggs have been added, reduce the heat to medium. When eggs float to the top, remove them with a slotted spoon and let drain briefly.

To assemble final dish: Toast bread slices and place on warm plates. Top each piece of toast with a slice of smoked salmon and a hot poached egg. Drizzle with yogurt sauce; garnish with parsley and capers.