Place eggs in large pot, cover eggs with water by one inch.
Place pot on stove and turn on heat to medium.
When water comes to a boil, turn burner off.
Place lid on pot and move pot to a burner that is not hot.
Set timer for 12 minutes for large eggs.
While eggs are cooking wash, peel and cut beet and place it in a medium pot with 2 cups water and 1 cup vinegar, and 1 teaspoon salt, bring pot with beet to a boil, reduce heat and simmer for 20 minutes.
When hard boiled egg timer goes off prepare an ice bath with 8 cups water 4 cups ice cubes and two teaspoons salt.
Gently place eggs into ice bath with slotted spoon or flat whisk for about 10 minutes until they are completely cooled.
Tap bottom of each egg on flat surface and peel eggs while in the cold water to help them peel smoothly.
Place beet pot over cold water bath for a few minutes to cool the liquid, then place the eggs into the beet juice or in a zipper bag and pour the beet juice over eggs and allow the eggs to sit in beet juice for an hour to color them vibrant and pretty pink in color.