I’d define “one song wonder” characters as characters who have little to no significance to the plot, but are instantly rememberable due to their awesome solo/songs. For example, some of my favorites are
Richard Henry Lee and Martha Jefferson from 1776
The Buffalo Bills from The Music Man
Nicely-Nicely Johnson from Guys and Dolls
Daniela, Carla, and The Pirague Guy from In the Heights
Alfred Doolittle From My Fair Lady
Ulla Bloom From The Producers
What are yours?