https://www.instructables.com/id/Printed-Shower-Knob/ In the comments, Studleylee indicated a method he used to repair such a handle (hopefully he will write his method up). This triggered an idea for repairing my original broken knob.
All I really needed was a way to hold the broken piece to the original part of the knob--a big fat washer would do the trick.
In "Primitives," you create a cylinder. The cylinder has a radius of 14mm and a height of 12mm.
"Draw" a circle in the center, radius 7.53mm.
"Extrude, Cut" the 7.53mm circle for 12mm.
Print it--takes 11 minutes and uses less than ten cents worth of plastic.