Place the eggs gently in a single layer in the bottom of a medium saucepan. If using fresh-from-fridge eggs, let them sit at room temperature for 5 minutes to reduce cracking.
Add cold water until it covers the eggs by about 1 inch. Add the vinegar if using (this helps loosen the shell from the membrane).
Place the pan over high heat and bring to a rolling boil. Once the water is boiling vigorously, start your timer for your preferred doneness:
6 minutes → soft, runny yolk
8 minutes → jammy yolk
10 minutes → fully set but still creamy yolk
When the timer ends, immediately remove the pan from heat and transfer the eggs (using a slotted spoon) into a bowl filled with ice water. Let them sit for at least 3 minutes or until fully cool to the touch—this “shock” halts cooking and helps create a gap between shell and membrane.
Tap each egg gently on a hard surface, then roll it under your palm to crack the shell all over. Peel under a stream of cool running water if desired; the shell should slip away easily, leaving smooth, intact whites.
Serve right away, or store unpeeled in the fridge for up to 7 days or peeled for up to 2 days.