The sentence that contains a nonrestrictive phrase is:
"My brother, always laughing at his own jokes, does not think I am funny."
In this sentence, the phrase "always laughing at his own jokes" is nonrestrictive because it adds extra information about "my brother" but is not essential to the meaning of the sentence. The sentence would still make sense if that phrase were removed: "My brother does not think I am funny." Nonrestrictive phrases are usually set off by commas.