Prepare the Berry Swirl: In a small saucepan, combine the mixed berries, lemon juice, granulated sugar, and honey.
Cook the Berry Mixture: Place the saucepan over medium heat. Stir gently and cook until the sugar is completely dissolved and the berries begin to soften and release their juices. This should take about 5-7 minutes.
Thicken the Berry Swirl (Optional): Continue to cook the berry mixture for another 5-8 minutes, stirring occasionally, until it thickens slightly to a syrupy consistency. Remove from the heat.
Smooth the Berry Swirl (Optional): If you prefer a smoother swirl in your ice cream, use an immersion blender to carefully blend the warm berry mixture until your desired consistency is reached. Be cautious when blending hot liquids. Alternatively, you can press the mixture through a fine-mesh sieve to remove seeds.
Chill the Berry Swirl: Pour the cooked berry mixture into a shallow bowl or container and let it cool completely in the refrigerator. This will take at least 2 hours. Make sure it's thoroughly chilled before adding it to the ice cream base.
Combine the Ice Cream Base: In a separate bowl, whisk together the heavy cream and whole milk until well combined.
Churn the Ice Cream: Pour the cream and milk mixture into your ice cream maker. Churn according to the manufacturer's instructions. This usually takes around 20-30 minutes, or until the mixture has thickened to a soft-serve consistency.
Add the Berry Swirl: Once the ice cream has finished churning, gently swirl in the chilled berry mixture. You can add it all at once or in layers for a more ribboned effect. Avoid overmixing, as this can cause the swirl to disappear into the ice cream base.
Freeze to Solidify: Transfer the ice cream into airtight containers. Place the containers in the freezer and freeze for at least 3 hours, or until the ice cream is firm enough to scoop.