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Zest the lemons; chop the zest. Juice the lemons.
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Place butter into a the top of a double boiler, over (not in) gently boiling water. As it melts, add sugar, lemon juice, and lemon zest. Stir frequently until butter is melted and sugar is dissolved.
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Strain the beaten eggs into the hot butter/sugar/lemon mixture, stirring constantly with a wire whip. Be patient; almost all the egg will eventually flow through. Straining introduces the egg at a slow rate, preventing curdling, and also leaves hard pieces of albumen behind.
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Continue to heat the lemon curd stirring constantly, until it thickens. It will coat a spoon and no longer taste "eggy". Pour into clean glass jars while hot, and refrigerate promptly.