Combine the berries with the sugar, using ¼ cup if they are very sweet and ½ cup if less so, in a small nonreactive saucepan and stir well. Put the pan over medium heat and cook, stirring frequently, until the berries are soft and the liquid they release has reduced somewhat, about 10 minutes.
Let cool slightly, then transfer the berries and their juice to a blender or food processor. Puree until smooth. Strain half the mixture through a fine-mesh strainer into a medium bowl, pressing on the solids to extract as much puree as possible. Discard the solids. Add the unstrained puree to the same bowl and stir once to combine. Cover the bowl and refrigerate.
Make the Base
In a medium heatproof bowl, whisk the yolks just to break them up, then whisk in half of the sugar (¼ cup). Set aside.
In a heavy nonreactive saucepan, stir together the cream, milk, salt and remaining sugar (¼ cup) and put the pan over medium-high heat. When the mixture approaches a bare simmer, reduce the heat to medium.
Carefully scoop out about ½ cup of the hot cream mixture and, whisking the eggs constantly, add the cream to the bowl with the egg yolks. Repeat, adding another ½ cup of the hot cream to the bowl. Using a heatproof rubber spatula, stir the cream in the saucepan as you slowly pour in the egg-and-cream mixture from the bowl into the pan.
Cook the mixture carefully over medium heat, stirring constantly, until it is thickened, coats the back of a spatula and holds a clear line when you run your finger across the spatula — about 1 to 2 minutes longer.
Strain the base through a fine-mesh strainer into a clean container. Set the container into an ice-water bath, wash your spatula, and use it to stir the base occasionally until cool. Remove the container from the ice-water bath, cover with plastic wrap and refrigerate the base for at least 2 hours or overnight.
Freeze the Ice Cream
Whisk the blackberry puree into the chilled base.
Freeze in your ice cream machine, according to the manufacturer’s instructions. Enjoy right away, or for a firmer ice cream, transfer to a chilled container and freeze for at least 4 hours.
From the Bi-Rite Creamery cookbook Sweet Cream and Sugar Cones