This is a 17th century recipe. Make syrup by boiling 2 cups water with 1 cup sugar till smooth. Only use real Parmesan, nothing domestic will do. Leftover syrup will last for ages, use to sweeten tea, or cold brewed coffee.
Mix eggs into a bowl and beat very light. Beat in grated cheese and stir to combine. Stir in syrup and cream. Cook in a double boiler, make sure that it doesn't curdle. Strain. Chill. Freeze in an ice cream maker, according to manufacturers instructions.
Transfer to a container, covered, to freeze entirely.