Preheat the oven to 350°F. Spread all of the walnuts on a baking sheet and toast until fragrant, 6 to 8 minutes. Coarsely chop in a food processor and set aside ½ cup.
Heat the cream and milk to boiling in a large saucepan. Add all the nuts but the ½ cup and let steep 2 hours. Strain the cream mixture through a cheesecloth-lined strainer or a kitchen towel, pressing the nuts to extract the maximum flavor. Return the cream to the saucepan, add ½ cup sugar, and heat to boiling, stirring to dissolve the sugar.
Whisk the egg yolks and the remaining ½ cup sugar until just combined. Whisk in about 1 cup of the hot cream mixture, then whisk into the remaining cream mixture. Cook over medium heat, stirring constantly, until thick enough to coat the back of a spoon, 3 to 5 minutes. Do not boil.
Strain the custard into a mixing bowl and place immediately in a larger bowl filled with ice water. Chill the custard well, preferably overnight in the refrigerator. Freeze in an ice cream maker according to the manufacturer’s instructions. Fold in the reserved ½ cup nuts just before the ice cream finishes freezing.