Cook the Blackberries. In a saucepan, combine the blackberries, half the sugar, and lemon juice. Cook over medium heat until the berries burst and become syrupy, about 8–10 minutes. Press the mixture through a fine-mesh sieve to remove the seeds. Cool the puree completely.
Prepare the Ice Cream Base. In a medium saucepan, whisk egg yolks (if using) with the remaining sugar until pale. Slowly add warm milk and cook over low heat, stirring constantly, until the custard thickens slightly and coats the back of a spoon. Don’t boil! Remove from heat and stir in heavy cream, vanilla, salt, and the cooled blackberry puree.
Chill the Mixture. Cover and refrigerate for at least 4 hours or overnight. Cold base = better texture when churned.
Churn. Pour the chilled mixture into an ice cream maker and churn according to your machine’s instructions (usually 20–25 minutes). The ice cream should thicken to a soft-serve consistency.
Freeze. Transfer the churned ice cream to an airtight container. Press parchment or plastic wrap on the surface and freeze for 2–4 hours or until scoopable.