Put quail eggs in a medium pot and cover with 2 in. cold water. Over high heat, bring to a boil, then simmer 5 minutes. Drain eggs and transfer to a bowl of ice water to cool. Crack shells all over, return to water, and let sit 2 minutes (this loosens the shells). Peel eggs.
Combine mayonnaise, wasabi to taste, sesame oil, soy sauce, and salt in a small bowl. Put furikake in another small bowl. Serve both with eggs for dunking.
*Find quail eggs at Asian and farmers' markets and furikake--a savory mix of sesame seeds, seaweed, and dried fish--at well-stocked grocery stores, Japanese markets, and amazon.com