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1
For the beet-pickled eggs: Put the cold eggs in a medium saucepan and cover with cold water.
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2
Heat the water to a boil, then cover the saucepan and remove it from the heat.
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3
Let stand for 12 minutes.
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4
Drain the eggs and rinse with cold water.
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5
Let the eggs cool a bit, then peel them while they are still warm (eggs are much easier to peel when warm).
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6
Place the hard-boiled eggs in a bowl or storage container and pour the pickling brine from the beet jars over the eggs, making sure the eggs are submerged.
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7
(You may need to place a weight or a plate on top.)
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8
Allow the eggs to sit for 45 minutes to 1 hour in the brine, but no longer or they'll start to get rubbery.
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9
For the sweet Hungarian filling: Mix together the mayonnaise, sour cream, dill, vinegar, horseradish, mustard, paprika and cucumber.
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10
Season with salt and black pepper.
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11
Slice the eggs in half lengthwise.
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12
Gently remove the yolks by pressing your thumb against the back of each yolk to pop it out of the white.
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13
Add the yolks to the bowl with the filling and mash with a fork until smooth.
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14
Season with salt.
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15
Spoon the filling into the egg whites, or use a re-sealable plastic bag to pipe it in.
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16
Sprinkle with paprika and dill before serving.
