The clause "who can cook" is an adjective clause, modifying man.
The larger clause (that you will marry a man who can cook) is the object of the sentence, and is a noun clause.
---
The clause "who can cook" is an adjective clause (aka relative clause), a group of words with a subject (who) and a verb (can cook) that is introduced by a relative pronoun, but does not express a complete thought. Example:
A man who can cook is a man after my own heart.
The clause "who can cook" is describing the noun "man".
An adverb clause is a group of words with a subject and a verb that is introduced by a subordinate conjunction, that does not express a complete thought.
He scrubbed the kitchen until everything shined.
The clause "until everything shined" is modifying the verb "scrubbed".
Note: Just like an adjective, an adjective clause describes a noun, and an adverb clause functions as an adverb.