Toast the walnuts in a dry skillet over medium heat until lightly golden and fragrant. Let them cool, then finely chop or grind them.
In a medium saucepan, combine the milk and heavy cream. Add the vanilla extract and the finely ground walnuts. Gently heat over medium heat until steaming, but do not boil.
In a separate bowl, whisk together the sugar and egg yolks until pale and creamy.
Slowly pour a ladleful of the warm milk mixture into the egg yolk mixture, whisking constantly to temper the eggs. This prevents the eggs from curdling.
Pour the tempered egg mixture back into the saucepan with the remaining milk mixture. Cook over low heat, stirring constantly, until the cream thickens and coats the back of a spoon (about 5-7 minutes). Do not let it boil!
Strain the mixture through a fine-mesh sieve to remove any large walnut pieces or thicker bits. Let it cool completely to room temperature, then refrigerate for at least 4 hours to allow the flavors to meld.
If you have an ice cream maker, pour the mixture into the machine and churn according to the manufacturer's instructions. If not, pour the mixture into a freezer-safe container and freeze, stirring with a fork every half hour to maintain a creamy texture.
Let the ice cream soften at room temperature for a few minutes before serving, to make it easier to scoop. Garnish with coarsely chopped walnuts or a drizzle of honey.
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