Peel the kiwis and mash them in a bowl until pureed. Stir 2 tablespoons sugar into the fruit, cover, and refrigerate 1 hour.
Whisk the eggs in a mixing bowl until light and fluffy, 1-2 minutes. Whisk in 1 cup sugar, a little at a time, then continue whisking until completely blended, about 1 minute more. pour in the cream and whisk to blend. stir in the kiwis.
Transfer the mixture to an ice cream Maker and freeze following manufacturer's instructions.