In a large bowl, whisk the egg yolks just enough to break them up. Gently heat the half-and-half and sugar in a nonreactive saucepan, stirring slowly over low heat until the half-and-half is steaming and the sugar is dissolved.

Drizzle the warm cream into the egg yolks, whisking constantly as you pour. (This is called tempering the egg yolks.)

Pour the mixture back into the saucepan. Measure the heavy cream into the mixing bowl. Cook the mixture over low heat, stirring slowly and scraping the bottom of the pan with a wooden spoon or heat resistant rubber spatula, until it thickens enough to coat the spoon.

Immediately remove from the heat and strain through a fine-mesh sieve into the bowl with the heavy cream. Whisk together to cool the mixture, cover, and chill thoroughly.

Stir the black currant syrup, lemon juice, and kirsch, if using, into the chilled ice cream mixture. Freeze, following the instructions for your ice cream maker.