Tom's mother is busy with breakfast.
即：
Tom's mother is busy cooking breakfast.
=Tom's mother is busy with breakfast.
be busy with sth 忙于做某事；忙于某事
be busy doing sth 忙着做某事.
补充：
"cook"除了是名词之外,还可以是动词：
cook [kuk]
vt.烹调,煮
vi.烹调,做菜
n.厨师,厨子.