Using a serrated knife, cut into the shell at the large end of the quail egg. Carefully open the shell and drop the egg into a small bowl. Repeat with the remaining eggs, each in its own bowl. Bring water and vinegar to a boil in a medium saucepan over high heat. Gently lower each egg into the boiling water and poach for 30 seconds, or until firm.

To serve, arrange 6 large soup spoons on 6 large plates. Using a slotted spoon, carefully transfer each poached egg to a soup spoon. Drizzle melted butter over the egg and top with roe. Sprinkle with chives.