Prepare an ice bath. In a medium saucepan set over medium heat, whisk together yolks, eggs, sugar, lemon juice, and zest.
Using a wooden spoon, stir constantly until mixture coats the back of the spoon, 7 to 8 minutes. Remove from heat; stir in cream and milk. Pour mixture through a fine sieve into a clean bowl. Chill over the ice bath or overnight in the refrigerator.
Freeze mixture in an ice-cream maker, according to manufacturer's directions. Place in an airtight container in the freezer; store up to 1 month.