4 cups blackberries
1-1/4 cups sugar
Juice of 1/2 lemon
1-1/2 cups half-and-half
5 egg yolks
1-1/2 cups heavy cream
In a medium saucepan, combine blackberries with 1/4 cup sugar and lemon juice. Cook over low heat until blackberries are broken down and all is juicy...about 20 minutes. Pour the mixture through a mesh strainer, forcing as much liquid through as you can. Set it aside to cool. Discard the blackberry pulp and seeds.
Heat the half-and-half and remaining 1 cup sugar in a saucepan over medium heat. In a separate bowl, whisk egg yolks. Temper the eggs by adding a bit of warm cream, whisking constantly. Pour the tempered yolks into the saucepan, stirring. Cook over medium-low heat until thick, stirring constantly until it has thickened. Don't over-heat or it will curdle.
Pour heavy cream into the bowl with the berry juice, then add custard and stir to combine. Refrigerate this mixture. Freeze in an ice cream maker.