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1
Cover beets with cold water by 1 inch in a 3-quart heavy saucepan and bring to a boil.
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2
Reduce heat and simmer beets, partially covered with lid, until tender, about 40 minutes.
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3
Transfer beets to a bowl with a slotted spoon (reserving them for another use), then measure out 2 cups beet cooking liquid, discarding remainder.
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4
Bring beet liquid to a boil in a small saucepan along with vinegar, sugar, salt, bay leaves, and cloves, stirring until sugar is dissolved.
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5
Remove from heat and cool pickling liquid completely, about 1 hour.
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6
While pickling liquid cools, cover eggs with cold water by 1 inch in a small saucepan and bring to a boil, stirring gently (to help center the yolks in eggs).
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7
Reduce heat and gently boil eggs, uncovered and undisturbed, 3 minutes (or 10 minutes for regular eggs).
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8
Pour off water and shake pan so eggs hit each other, lightly cracking shells.
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9
Cover eggs with cold water and let stand 15 minutes (to stop cooking and facilitate peeling).
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10
Drain and peel eggs, then transfer to a glass jar or deep bowl.
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11
Reserve 2 tablespoons pickling liquid (for watercress salad vinaigrette; recipe precedes) and pour remaining liquid over eggs.
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12
Let eggs (quail or regular) pickle, covered, 24 hours.
