It took longer to ask that question than it did to find the answer for myself.
1 1/4 cups white wine vinegar
1 1/4 cups rice vinegar
1 1/4 cups water
1/2 cup sugar
5 to 6 bay leaves
1 teaspoon whole black peppercorns
1 lemon wedge
1 tablespoon sweet or hot paprika
24 quail eggs
Directions:
In a large pot over medium-high heat, combine all the ingredients except the quail eggs. Cook for 15 to 20 minutes; the liquid should be at a low boil. Set aside to cool slightly. Discard the lemon wedge and bay leaves.
Have ready a bowl of ice-cold water, a cloth napkin and a sterile jar with a tight-fitting lid. The jar should be large enough to hold the peeled eggs and the cooked liquid.
Place a cloth napkin on the bottom of a separate large pot and place the eggs on the napkin. Cover with water by an inch or so and bring to barely a boil over medium heat. Remove from the heat, cover and let sit for 4 to 5 minutes, then use a slotted spoon to transfer the eggs to the cold-water bath until they are cool enough to handle, 2 to 3 minutes. Carefully peel the eggs and let them come to room temperature. Place the eggs in the jar and add the reserved cooking liquid. Seal tightly and wrap the jar in the napkin.
Bring a large stockpot of boiling water to a boil over high heat. Make sure the jar is covered with water by at least 2 inches. Carefully place the jar in the boiling water, weighing it down with something that will keep the jar stationary. Boil for 35 to 40 minutes. Turn off the heat and let the water cool to about room temperature. Refrigerate the jar of eggs until ready to serve.