The sentence that correctly uses a nonrestrictive clause is:
My friend watched a movie yesterday—my favorite one.
In this case, "my favorite one" is a nonrestrictive clause that adds extra information about the movie without restricting or changing the identity of the noun it describes.
To clarify the other sentences:
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Her oldest sister, Mallory, has a wonderful singing voice. - This has a nonrestrictive clause but is incorrectly formatted. The comma before "Mallory" is necessary.
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The dog, who is black and brown, jumped over the fence. - Similar to the previous sentence, it's incorrectly formatted without the commas.
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I like to eat pizza best with extra cheese while it is hot. - This sentence is grammatically incorrect as it lacks proper punctuation.
Thus, the best choice provided, despite the other sentences needing adjustments for correct punctuation, is "My friend watched a movie yesterday—my favorite one."