Place two halves of ham on each half-slice of bread. In small saucepan, stir together mustard, cheese, and sauce. Cook over low heat, stirring constantly until thoroughly heated. Set aside and keep warm.

In 12-inch skillet, bring 2 to 3 inches of water to boiling. Reduce heat to keep water gently simmering. Break cold eggs, 1 at a time, into custard cup or saucer. Holding dish close to water’s surface, slip eggs 1 by 1 into water. Cook until whites are completely set and yolks begin to thicken but are not hard, about 3 to 5 minutes. With slotted spoon, lift out eggs. Drain in spoon or on paper towels. Trim any rough edges, if desired. Place eggs on ham. Spoon about 2 tablespoons sauce over each egg. Garnish with red cabbage, nectarine, and parsley if desired. Serve immediately.