Place eggs in a medium saucepan; cover with cold water. Heat over medium heat to boiling. Reduce heat to low; simmer, uncovered, about 15 minutes. Remove from heat; run cold water into pan until cool. Let eggs cool in cold water. Drain. Lightly tap shells all over with back of spoon; do not crack so hard that shells actually come loose.

Return eggs to saucepan; add remaining ingredients. Add cold water to cover egg; heat over medium heat to boiling. Reduce heat to low; simmer, covered, about 1-1/2 hours.* Remove from heat. Let cool to room temperature in cooking liquid.

Refrigerate eggs, in cooking liquid, until serving time**. At serving time, drain eggs, discarding liquid; shell eggs and leave whole or cut in half.

* Heat may be turned off at any time and cooking resumed later

** The longer the eggs soak, at least several hours, the better flavor they will have. They can be done several days in advance.