Beat eggs and sugar together until fluffy. Add vanilla. Add half and half, and heavy cream. Mix well until top of mixture is frothy in appearance.
Put ice cream mixture in a plastic container, and put in fridge and chill thoroughly. Puree strawberries. Put purred strawberries in a separate container, and chill in fridge.
Freeze ice cream mixture in ice cream freezer 25-30 minutes. While canister is turning during freezing process, pour pureed strawberries in the canister. If ice cream is not thick enough, remove from canister and put in plastic storage container and put in freezer still stiff.