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1
Place 1 3/4 cups of the half-and-half, the sugar, and the salt in a medium saucepan over medium heat and stir until the sugar has completely dissolved, about 3 to 4 minutes.
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2
Meanwhile, pour the remaining 1/4 cup half-and-half into a small bowl.
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3
Sprinkle the gelatin evenly over the surface and let stand without disturbing until the gelatin softens, about 3 minutes (it will start to look wavy and wrinkled).
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4
Place the egg yolks in a medium heatproof bowl and whisk until smooth, about 1 minute.
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5
Remove the half-and-half mixture from the heat and slowly pour about half of it into the egg yolks, whisking constantly until incorporated.
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6
Pour the half-and-half/egg mixture back into the pan and add the gelatin mixture and the butter.
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7
Cook over low heat, whisking constantly, until the butter melts, the gelatin dissolves and no longer feels grainy, and an instant-read thermometer registers 160 degrees F, about 5 minutes.
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8
(Do not let the mixture boil or go above 170 degrees F, or the gelatin will not set properly and the eggs may curdle.)
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9
Remove the saucepan from heat and stir in the vanilla.
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10
Set a fine-mesh strainer over a medium heatproof bowl and pour the mixture through the strainer.
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11
Discard the solids.
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12
Divide the mixture among the pop molds and freeze until frozen, about 3 hours.
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13
Alternatively, to serve as pudding, divide the mixture among ramekins and refrigerate until set, about 3 hours.
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14
(To avoid the skin that forms on the surface of pudding, cover each ramekin with plastic wrap and make sure its directly touching the pudding.)
