Make the ice cream base:

1. In a medium saucepan, combine the heavy cream, whole milk, and granulated sugar. Heat over medium heat until the mixture is warm but not boiling. Stir occasionally to dissolve the sugar.
2. In a separate bowl, whisk the egg yolks until smooth. Slowly pour a small amount of the warm cream mixture into the egg yolks while whisking constantly to temper the eggs. Gradually add the rest of the cream mixture to the eggs while continuing to whisk.
3. Return the combined mixture to the saucepan and cook over low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon (about 5-7 minutes).
4. Remove from heat and whisk in the cocoa powder and chopped bittersweet chocolate until smooth and fully incorporated.
5. Transfer the mixture to a clean bowl and let it cool to room temperature. Once cooled, cover and refrigerate for at least 4 hours, or overnight, to chill completely.

Make the crimson berry swirl:

1. In a small saucepan, combine the mixed berries, sugar, and lemon juice. Cook over medium heat for about 5-7 minutes, stirring occasionally, until the berries break down and the mixture thickens into a syrup.
2. Remove from heat and allow the berry mixture to cool completely. Once cooled, strain it through a fine mesh sieve to remove seeds, if desired, and set the syrup aside.

Assemble and churn the ice cream:

1. Once the ice cream base has chilled, pour it into an ice cream maker and churn according to the manufacturer’s instructions.
2. In the last few minutes of churning, add the chopped chocolate chunks to the ice cream.
3. Once churned, transfer the ice cream to a storage container. Swirl in the crimson berry syrup, creating ribbons of berry goodness throughout the ice cream.
4. Cover and freeze the ice cream for at least 4 hours, or until firm.

Serve and enjoy:

1. Scoop the ice cream into bowls or cones and enjoy the rich chocolate and berry combination!