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1
Combine the vinegar, water, beet, sugar, measured salt, and pickling spice in a small saucepan and bring to a boil over medium-high heat, stirring to dissolve the salt and sugar.
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2
Remove the pan from the heat and let sit until the mixture cools to room temperature, about 30 minutes.
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3
Meanwhile, place the eggs in a medium saucepan with a tightfitting lid and cover with cold water by 1 inch.
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4
Place over high heat and bring to a boil.
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5
Immediately remove the pan from the heat, cover, and let sit 3 minutes.
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6
Prepare an ice water bath by filling a large bowl halfway with ice and water.
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7
When the eggs are ready, transfer them with a slotted spoon to the ice water bath.
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8
Let sit until the eggs are cold, about 5 minutes.
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9
Carefully crack and peel each egg and rinse under cold water to remove any residual shell pieces.
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10
Pat the eggs dry with a paper towel and transfer them to a glass pint jar with a tightfitting lid; set aside.
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11
Set a fine-mesh strainer over a 1- or 2-cup measuring cup with a spout.
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12
Pour the cooled pickling liquid into the strainer and discard the contents of the strainer.
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13
Pour the pickling liquid over the eggs and seal the jar.
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14
Turn the jar upside down a few times to distribute the pickling liquid.
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15
Refrigerate at least 24 hours and up to 1 week.
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16
Serve the pickled eggs sprinkled with coarse salt.
