1. Whisk the eggs until smooth in a saucepan, then whisk in the cream and simple syrup. Warm over low heat, stirring constantly, until it thickens at about 170°F (76°C) and coats the back of a spoon.
2. Remove from the heat, whisk in the grated parmesan until melted, then strain through a sieve into a bowl. Cool to room temperature, with parchment or plastic wrap pressed on the surface to prevent a skin.
3. Pour into a CREAMi pint and freeze for 24 hours. Spin on the Ice Cream program, adding a re-spin if the texture is crumbly.