The correct option is A agreeing to a large slice of cherry pie even though he was full to the point of bursting
A participle is that form of the verb which partakes of the nature both of a Verb and of an Adjective.
A participle phrase will begin with a present or past participle. If the participle is present, it will dependably end in ing. Likewise a regular past participle will end in a consistent ed.
Since, all phrases require two or more words, a participle phrase will often include objects and/or modifiers that complete the thought.
Participle phrases always function as adjectives,adding description to the sentence.
In this case,
Option B is correct. The present participle phrase, 'agreeing to a large piece of cherry pie even though he was full to the point of bursting' describes the noun 'Cooper'.
Option A is incorrect because it is the main clause having a subject and a predicate of its own.
Option C is incorrect because it functions as a subordinate clause.
Option D is incorrect because it is just a phrase devoid of any participle.