In case you haven't run across the word before, a "pastiche" is "a work of visual art, literature, music, or architecture that imitates the style or character of the work of one or more other artists, and, unlike parody, pastiche pays homage to the work it imitates, rather than mocking it."
So there!
Did you know there's a Betty Boop musical headed to Broadway? I bet they don't have a scene like this, though: