GE profile cooking range traditional glass cooktop not working properly
The OP said he already tried power cycling it just in case it was some transient controller problem, so my next best guess would be that the switch is bad.

It looks like it's the switch marked part number 20 "Dual Burner Control Switch" on the product diagram on the parts page he linked to. Several people on the comments page for that switch said they had the same problem before replacing the switch -- the burner stays on high.

If a wiring diagram of the stove (or switch) is available, you should be able to test the switch with a multimeter. This site gives some guidelines, basically you're just testing for continuity between the switched terminals. With a switch like this that has multiple outputs (and possibly an independent indicator light output), it would be difficult to test it without knowing which terminal is which.