Finely chop the walnuts. Toast them in a dry skillet over medium heat for 2-3 minutes, or until fragrant. Set aside to cool.
In a medium saucepan, heat the milk, heavy cream, sugar, and cocoa powder over medium heat until the sugar is completely dissolved.
Add the finely chopped dark chocolate and stir until completely melted and smooth.
In a separate bowl, whisk the egg yolks. Gradually add a small amount of the hot chocolate mixture to the yolks, tempering them to prevent curdling.
Pour the tempered egg mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens slightly (about 5 minutes).
Remove from the heat and stir in the vanilla extract and rum. Let it cool completely.
Pour the mixture into an ice cream maker and churn 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 it in the freezer. Stir every 30 minutes to prevent ice crystals from forming.
When the ice cream begins to solidify, stir in the toasted walnuts. Let it freeze completely (about 4-5 hours).
Before serving, let it soften slightly. Garnish with extra walnuts or chocolate shavings.
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