Grammatically, the term functions as a compound noun phrase. The core noun is "holiday," which is modified by the preceding words. "Food" acts as an attributive noun (a noun used as an adjective) to specify the type of holiday, and "September 11" functions as an adjectival phrase indicating the specific date. The main point of any discussion on this topic would therefore be a specific type of holiday.
No officially recognized or widely observed food-centric holiday is associated with September 11th. In the United States, this date is formally known as Patriot Day, a National Day of Service and Remembrance. It is a solemn occasion dedicated to commemorating the victims of the 2001 terrorist attacks and honoring the first responders and heroes. The established tone of the day is one of reflection, mourning, and patriotism, which is fundamentally incongruous with the celebratory nature of a typical food holiday. While some minor, unrelated food observances, such as National Hot Cross Bun Day, may fall on this date by coincidence, they are not linked to the historical significance of 9/11.
For practical application, such as in content creation or marketing, focusing on the phrase as a "food holiday" is inappropriate and risks being perceived as insensitive. The critical takeaway is that while the grammatical components identify a specific concept, the cultural and historical context of the date overrides any such classification. Any analysis must prioritize the date's significance as a day of remembrance over its potential as a theme for a culinary celebration.