eat 作为不及物动词，后接of 介词短语，表示吃某种食物。例如：

Harold would really eat of that good, sweet yogurt. I don't eat so much of it now.

In short, by all means eat of the fruit, but take care not to destroy the fruitfulness.

I ask them in here of an afternoon sometimes, and they eat of what I fix them-hot biscuits and my blackberry jam, baked apples, with the thick yellow clotted cream spooned over and honey on top, till they're full as ticks.

所以，网友的这个句子中：

He ate sparingly and simply, of the same food his men were given—consisting usually of cabbage, noodles, beans, mutton, and sometimes bread.

of the same food为状语修饰ate, 表示吃的食物种类。his men were given为定语从句修饰the same food.

consisting of为现在分词短语，也修饰food.为非限制性定语。