#1 is correct. #2 is wrong. These are correct: "There is a variety of food" "There are varieties of food" If you want to use "food" as a plural, do it like this: "There are various foods" "There are many different foods" "There are diverse foods"

Quote from a grammar dictionary: "Use is if you want to emphasize the group; use are if you want to emphasize the individual members. It's the same with other collecting phrases, like a variety of. There is a wide variety of flavors to choose from. There are a variety of unique destinations we can visit." "As a collective noun, variety, when preceded by a, is often treated as a plural: A variety of inexpensive goods are sold here." I will aquiesce. Given the need for folks to be right, go ahead. Fill yer boots. Italki is no longer a language-learning forum. It's an egocentric forum. Ciao!

2 is correct because if it’s plural it’s are if it’s singular it’s is.

1 - If you want to emphasize food as a group. In other words, not individual items of food, just "food." There is a variety of food at our restaurant. 2 - If you want to use the collective noun "variety" as a plural preceded by 'a.' There are a variety of unique foods to try at our restaurant.