Bring a large pot of water to a boil. Prepare an ice-water bath fitted with a sieve and set aside. Using a serrated knife carefully cut off one-third of the shell from the widest end of each egg taking care not to break the yolks. Transfer to a medium bowl. Add enough vinegar to saucepan until you can smell it, about 1/4 cup. Using a spoon, stir boiling water to create a swirling motion and carefully add eggs to water. Cook until whites are just set, about 1 minute. Drain and transfer eggs to ice-water bath to cool. Trim whites using kitchen shears so that you have 30 individual poached quail eggs.
Transfer a quail egg to each slice of toast; garnish with caviar, if desired.