1 Bring to a rolling boil over high heat, then reduce heat to a lower medium boil for an additional 12 minutes. 2  Promptly place eggs in ice water to chill so egg yolks remain nice and bright yellow.3  Hard boiled eggs are good for one week if kept in the shell in the refrigerator.heck out the FAQ page for answers. 1  To hard cook eggs, place in enough cold water to cover eggs completely. 2  Bring to a rolling boil over high heat, then reduce heat to a lower medium boil for an additional 12 minutes. 3  Promptly place eggs in ice water to chill so egg yolks remain nice and bright yellow.