Heat the cream, milk, sugar and walnut pieces in a heavy-bottomed pot to 170 degrees, or to the point at which it steams but does not simmer. Turn off the heat, add the vanilla bean and the scraped insides of the bean, stir well and cover. Let this cool for 1 hour.
Move the mixture to a container and refrigerate for at least 4 hours, or up to overnight.
Strain the mixture to remove the vanilla bean and the walnut pieces. Reserve the walnut pieces and set them in the fridge.
Heat the strained mixture to 160°F. As it is heating, beat the egg yolks to combine. When the cream has hit its temperature, you will need to temper your eggs so they don’t scramble. One hand holds a ladle, the other whisks the egg yolks: Pour in a little hot cream with one hand, whisking vigorously with the other. Pour in 2 ladles full, then pour the egg-cream mixture into the pot and stir well. Cook this gently, stirring often, for 5 minutes. Do not let it simmer.
Strain this one more time and chill the mixture down at least to room temperature before putting into the ice cream maker. Churn it until it has the consistency of soft-serve ice cream, then remove to a large bowl and gently fold in the reserved black walnut pieces. Freeze and eat!
Note that the prep time does not include chill time or the time it takes to churn your ice cream.