In a medium saucepan, combine sugar and water and bring it to a boil. Continue to boil until the sugar has dissolved completely, stirring occasionally. Add the dates and salt and boil for 3 minutes. Remove saucepan from heat and let dates sit for 5 minutes to cool.
Use a food processor to puree the mixture until smooth. Transfer back to saucepan.
Add whole milk and 1 cup heavy cream to the date mixture. Pour remaining heavy cream into a large bowl and set aside.
Over a medium-low heat, stir date mixture until it just barely starts to simmer, then remove from heat.
In a small bowl, whisk together the egg yolks. Slowly pour ½ a cup of warm date mixture into the eggs and continue whisking until eggs have tempered.
Pour tempered eggs back into saucepan and turn up heat to medium. Stir constantly with a heatproof spatula until a custard forms and thickly coats the back of the spatula, about 8 minutes. Remove from heat and immediately pour into the large bowl with the remaining heavy cream. Stir well until custard cools, then transfer to refrigerator and chill for at least 4 hours or up to overnight.
Churn ice cream based on your ice cream maker manufacturer's instructions. Fold in walnuts and freeze overnight.