For yellow/classic deviled eggs: Put the eggs in a large saucepan in one layer with cold water to cover by 1 inch. Bring to a simmer and reduce heat to low. Cook at a bare simmer for 10 minutes, then immediately run under cold water to stop the cooking. When cool, peel the eggs and halve them lengthwise.
Put the egg yolks in a bowl with the mayonnaise, pickle brine, mustard, sugar, hot sauce and 1/4 teaspoon salt. Mash with a fork until smooth. You should have a heaping cup of egg mixture; divide it into 6 portions.
For yellow eggs: Stuff 4 egg whites with 1 portion of the yolk mixture and set aside.
For red eggs: Mash 1 portion of the yolk mixture with the paprika and stuff into 4 egg whites. Coat the filling with the chopped red pepper.
For orange eggs: Cook the baby carrots and saffron in a small saucepan with water to cover until tender. Drain, reserving the water, cool the carrots and chop. Fish the saffron threads from the water and add them along with the carrots to 1 portion of the yolk mixture. Mash well and stuff into 4 egg whites. Coat the filling with the shredded carrots.
For green eggs: Mash 1 portion of the yolk mixture with the avocado, parsley and lime juice and stuff into 4 egg whites. Coat the filling with more parsley.
For blue eggs: Stuff 4 egg whites with 1 portion of the yolk mixture. Coat the filling with the crushed chips.
For purple eggs: Finely chop about 1 tablespoon of the cooked beet and mash with the remaining portion of the egg yolk mixture. Stuff the filling into the 4 remaining egg whites. Slice the remaining beet and use to top the eggs.
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