What part of speech is drowses?

Drowses can be categorized as a noun and a verb.

Parts of speech

1. drowses is a verb, present, 3rd person singular of drowse (infinitive).
2. drowses is a noun, plural of drowse.

Verb
drowse - be on the verge of sleeping; "The students were drowsing in the 8 AM class"
drowse - sleep lightly or for a short period of time
Noun
drowse - The state of being sleepy and inactive.