In medium saucepan, combine 2 cups of the whipping cream, sugar, corn syrup and eggs; mix well.
Cook over medium heat 12 to 14 minutes or until slightly thickened, stirring constantly.
Remove from heat.
Cool completely.
When ready to freeze, stir in remaining 1 1/4 cups whipping cream, champagne and vanilla.
Prepare ice cream freezer and freeze according to manufacturer's directions.
In food processor bowl with metal blade or blender container, process strawberries until smooth.
Strain if desired; discard seeds.
In small saucepan, combine strawberries and cornstarch.
Cook over medium heat 5 to 8 minutes or until slightly thickened.
Cool; cover and store in refrigerator.