In a medium saucepan, combine the milk, heavy cream, and sugar. Heat over low heat, stirring until the sugar is completely dissolved.
In a separate bowl, whisk the egg yolks. Gradually add a small amount of the hot milk mixture to the egg yolks, tempering them.
Pour the tempered egg yolk mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens slightly (about 5 minutes).
Remove from heat, stir in the vanilla extract, and let cool completely.
Meanwhile, in a blender, combine the raspberries, strawberries, blueberries, honey, and lemon juice. Blend until smooth.
Pour the ice cream base into an ice cream maker and process according to the manufacturer's instructions until creamy.
If you don't have an ice cream maker, pour the mixture into a shallow dish and place in the freezer. Stir every 30 minutes to prevent ice crystals from forming.
When the ice cream is almost solid, swirl in the berry puree to create a marbled effect.
Melt the dark chocolate over a double boiler, then stir in the coconut oil until smooth and glossy.
Pour the melted chocolate over the top of the ice cream and return to the freezer for another 30 minutes to allow the chocolate to harden.
Let the ice cream stand at room temperature for a few minutes before serving. Slice and garnish with fresh berries.
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