Place quail eggs in a single layer in a saucepan
Add enough cold water to cover the eggs by about 1 inch
Bring the water to a gentle boil over medium-high heat
Reduce to a simmer once boiling starts
Boil for 2 to 4 minutes
For soft-boiled eggs, cook for 2 to 3 minutes
For hard-boiled eggs, cook for 4 minutes
Prepare an ice bath in a bowl with cold water and ice
Transfer the eggs to the ice bath immediately after boiling
Let the eggs cool for 5 to 10 minutes
Peel the eggs carefully by gently cracking the shell all over
Rinse under running water if needed to help remove the shell