Boil the quail eggs: Bring a pot of water to a gentle boil and carefully lower the quail eggs using a spoon. Boil for about 4 minutes, then transfer them immediately into a bowl of ice water to stop the cooking. Once cool, gently peel the eggs — quail shells can be delicate, so it helps to lightly roll them on the counter before peeling.
Prepare the pickling brine: In a small saucepan, combine vinegar, water, sugar, salt, garlic, peppercorns, mustard seeds, chili flakes, and bay leaf. If you’d like a beautiful pink hue, add a few slices of beet. Bring this mixture to a boil, then reduce the heat and let it simmer for about 3–4 minutes, stirring occasionally until the sugar and salt dissolve completely.
Combine and pickle: Place the peeled quail eggs in a clean glass jar. Carefully pour the hot brine over the eggs, making sure they are fully submerged. If using beet, you’ll notice the color gradually infuse into the eggs over time. Allow the jar to cool to room temperature before sealing it tightly.
Refrigerate and wait: Store the jar in the refrigerator for at least 3 days before eating. The longer you let them sit, the stronger and tangier the flavor becomes. After about 5 days, the eggs will have fully absorbed the brine and will be perfectly seasoned and ready to serve.