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Comments about Oaxaca
Many of the vegetarian restaurants in Mexico focus heavily on either eggs and cheese, and/or are limited to uninteresting hot dogs and veggie burgers. I would recommend just eating at taco carts on the street, which have more variety. Some may only have beans and/or avocado, but many also have corn, huitlacoche (a sort of mushroom/fungus that grows on corn), potatoes, or more. In Oaxaca, watch out in particular for tlayuda - the traditional flat tortilla/pizza sort of dish that comes with beans, onions, avocado, and cream (which you can get without). Oaxaca is known for putting lard (manteca) in its beans and spreading additional lard on top of the tlayuda dish.