Hi Erika!
Thank you for visiting the Moms Panel!
Unlike the Tomorrowland Terrace Fireworks Dessert Party in the Magic Kingdom, it is not possible to purchase a ticket to view Illuminations in a private area at Epcot while enjoying amazing desserts.
However, you may book your own, private, Illuminations Dessert Party through
Disney Catered Events (321-939-7278). To be able to do this you must be staying at a Disney Resort, and there will be a minimum number of guests required for this event. This would be a fun choice for a larger party, or celebration.
If you have any other questions, please come back and ask me - I would be happy to help you plan your magical vacation!