Now we are fully prepared for reasoning the meaning of 盤 - a 皿 used to carry or move stuffs around.
Its Simplified version 盘 uses 舟 instead of 般 comparing to its Traditional version 盤. Thus 盘 actually lost the correct context for its proper meaning.
And it should be understandable that 盘 | 盤 is usually shallow and flat to make it easier to carry foods or other kitchenwares around. A typical 盘 is shown below:
|盘 | 盤|
And Some other 盘 | 盤 which is used to carry foods:
|盘 | 盤|
|Learn one Chinese Character a day - 盘 | 盤|
Its Bronze Script is exactly composed of (which is 般) and (which is 皿).
Based on its original meaning, Chinese ancestors started to extend it to include more meanings.
盘 | 盤 is extended to refer to anything shallow and flat which is used to hold something else, like chess board - 棋盘.
盘 | 盤 is then used as a Chinese Classifier (https://en.wikipedia.org/wiki/Chinese_classifier) to describe number of dishes: 一盘菜, or anything else on a 盘 | 盤, like 一盘棋.
盘 | 盤 naturally has the meaning of 般, so 盘 | 盤 contains meaning of move. And from the meaning of move, 盘 | 盤 is extended to contain the meaning of "Count or Verify in details (by moving items one by one)"
While a person sits like following picture by crossing his legs, it is kind of forming a 盘 | 盤 to hold himself. So 盘 | 盤 eventually contains the meaning of "to cross or to wind"