Place a medium-size colander in the sink.

In a medium-size microwave safe bowl, heat 4 cups of water to boiling, about 5-6 minutes. Carefully add onions to the hot water. Use a large spoon to make sure onions are submerged. After 15 seconds, pour onion into the colander to drain. Transfer onion and lime slices to a jar (or jars) that will contain the onions (about a 3 cups capacity). You want the onions to fill the jar to the brim, but not be super tightly packed.

Combine vinegar, sugar, salt, peppercorns and coriander seeds in the previously used bowl. Stir and cook on high for three minutes. Remove from microwave, add fresh lime juice and stir to make sure all of the sugar and salt is dissolved.

Pour hot solution over the onions. Add enough water to bring liquid level to the top of the jar. Watch the beautiful color transformation take place; it's amazing!! Cover the jar(s) and allow to cool for 30 minutes then refrigerate. They can be eaten right away, but the ingredients will meld and the flavor will be even better if allowed to sit for 2-3 hours. Onions will keep well in the refrigerator for 5-7 days.