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1
Combine the blackberries, 1/4 cup sugar and the lemon juice in a saucepan.
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2
Cook over low heat until the blackberries are broken down and syrupy, about 20 minutes.
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3
Pour the mixture through a fine-mesh strainer into a bowl, using a whisk or spoon to force as much of the deep purple liquid through as you can; set aside to cool.
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4
Discard the blackberry pulp and seeds.
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5
Heat the half-and-half and the remaining 1 cup sugar in a saucepan over medium-low heat.
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6
Meanwhile, whisk the egg yolks in a bowl until pale yellow and thick.
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7
Temper the egg yolks by splashing in a very small amount of the warm half-and-half mixture while whisking constantly.
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8
Slowly pour the tempered yolks into the saucepan with the half-and-half and cook over medium-low heat, stirring constantly, until thick enough to coat the back of a spoon, about 5 minutes.
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9
Stir the heavy cream into the bowl with the berry mixture, then pour in the egg mixture and stir to combine.
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10
Churn in an ice cream maker (in batches, if necessary) according to the maker's instructions.
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11
Chop the chocolate into chunks and stir into the ice cream.
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12
Transfer to a freezer-safe container and freeze for several hours or overnight.
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13
Photograph by Kana Okada