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Place eggs in a single layer in a saucepan and cover with 1 inch of water. Add 1/2 teaspoon salt. Bring to a boil. Cover and remove from heat.
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Let stand for 15 minutes. Drain water and replace with cold water and ice. Let eggs cool for 5 minutes.
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Peel eggs. After you peel each egg, lightly rinse it to make sure you remove all shell bits. Then place the egg on paper towels.
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Slice eggs in half lengthwise. Remove yolks and place yolks in a medium bowl. Place egg whites on a serving platter.
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Mash yolks with a fork until finely crumbled. Add goat cheese, mayonnaise, tarragon, remaining 1/4 teaspoon salt, and pepper. Stir until well combined and smooth.
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Fill egg whites with yolk mixture. Use a piping bag or spoon mixture into each one. Garnish with minced tarragon.
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Chill deviled eggs prior to serving (cover lightly with plastic wrap or in a sealed container).