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?
Amos Hart from "Chicago" comes to mind.