What is the meaning of "(be) in the middle of sth / to be in the middle of doing sth" ?
Can I call you back? I'm in the middle of a meeting.

I can't do that now. I'm in the middle of cooking dinner.

Question

What is the meaning of "(be) in the middle of sth / to be in the middle of doing sth" ?
Can I call you back? I'm in the middle of a meeting.

I can't do that now. I'm in the middle of cooking dinner.

Answer

I'm in the middle of [X]. = I am [X]-ing right now/at this moment.

I'm in the middle of cooking dinner. = I am cooking dinner right now/at this moment.

[X] has a start, middle, and end.

I just started cooking dinner.
I'm in the middle of cooking dinner.
I just finished cooking dinner.

Answer

You use the verb "to be" to indicate the state of the subject.  e.g. I am happy.  I was angry. She is busy.

In this case, the adjective is a phrase "in the middle of cooking dinner"