In a saucepan, combine the milk, heavy cream, and sugar. Heat over medium heat, stirring until the sugar is completely dissolved. Do not boil.
Add the Nutella and stir constantly until it's completely melted and fully incorporated into the mixture.
Remove from heat and stir in the vanilla extract.
Let the mixture cool completely to room temperature, then refrigerate for at least 2 hours to chill thoroughly.
Pour the well-chilled ice cream base into an ice cream maker and churn according to the manufacturer's instructions. If you don't have an ice cream maker, pour the mixture into a freezer-safe container and stir it with a fork every hour to prevent ice crystals from forming.
Place the ice cream in the freezer for at least 4 hours to firm up completely.
Before serving, let it stand at room temperature for a few minutes to soften slightly for easier scooping. Garnish with toasted hazelnuts or a drizzle of extra Nutella.
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