Peel, core and cut apples into small pieces. Place apples in a gallon size ziplock bag. Pour into the bag a 1/4 cup of Celia's Pear Lime Cinnamon White Balsamic Vinegar. Squeeze out all the air and zip the bag shut. Place bag into refrigerator for 60 minutes turning the bag every 10 minutes to marinade the apples.
Preheat oven to 350°. In a large bowl, mix the eggs, sugar, cinnamon and oil. Add the apples and vinegar to mixture in bowl (coating as you go) Mix together the baking soda and flour and add to the ingredients in the bowl. Mix well (best with a fork) until all of the flour is absorbed by the wet ingredients. Pour mixture into a greased one 9x13 or two 9" round pans. Bake for approximately 55 minutes.