No matter what size eggs you use, the instructions are roughly the same. To hardboil eggs, put them in a pan in a single layer. Add enough cold water to just cover them. Using high heat, bring to a rapid boil. Immediately remove from heat. Cover and let stand only 15 to 20 minutes. Extra-large eggs will need about 20 minutes, no more. When time's up, pour out the hot water. Run cold water over them or cool them in ice water. Cool eggs quickly and don't overcook them. Then you won't have that ugly greenish ring.
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