Dissolve gelatin in boiling water in a bowl. Beat corn syrup, champagne, and egg whites into gelatin mixture; pour into a 9x13-inch pan. Freeze until firm, about 2 hours.
Spoon 1/2 of the mixture into a food processor or blender; cover and process on high speed until smooth but not melted, about 30 seconds. Pour mixture into a 9x5-inch loaf pan. Process remaining mixture and pour over mixture in loaf pan. Cover and freeze until firm, 6 hours to overnight.