Step 1

Boil syrup in a 2-quart heavy saucepan over moderately high heat until reduced to 3/4 cup, 5 to 10 minutes. Stir in cream, milk, and salt and bring to a boil over moderate heat.

Step 2

Whisk eggs in a large bowl, then add hot cream in a slow stream, whisking. Transfer to saucepan and cook over moderately low heat, stirring constantly, until slightly thickened and an instant-read thermometer registers 170°F, 1 to 2 minutes (do not let boil).

Step 3

Pour custard through a fine sieve into a clean metal bowl, then cool, stirring occasionally. Chill, covered, until cold, at least 3 hours.

Step 4

Freeze custard in ice-cream maker until soft-frozen, then, with motor running, add nuts. Continue churning ice cream until frozen, then transfer to an airtight container and put in freezer to harden.