Here is the fragment again:
And grabbed the last glazed doughnut while Frederick was pouring her a cup
of coffee.
You correctly identified the fragment as a lonely verb phrase. Grabbed, the verb which is missing a subject, is the clue.
To fix this fragment, you could add a subject, like this:
And Laurie
grabbed the last glazed doughnut while Frederick was
pouring her a cup of coffee.
Or you could use Punctuation Rule 8:
Main Clause + Ø + Lonely Verb.
The correction would look like this:
Laurie complained about her caffeine headache
and grabbed the last glazed doughnut while Frederick
was pouring her a cup of coffee.
Enjoy having your own personal knight!