Anyone put a variable control into a Broan Vented Stove fan?

If it is already too loud on low, it will be too loud with a variable speed switch. Think of it as variable noise. I'd try the dimmer, just be sure it is rated for the motor load.

The ideal solution, of course, it to get a unit with the motor mounted on the outside wall and just a duct indoors.

I have one with a variable speed controller built into the hood. All was by Nutone/Broan. And, of course, slowing it down does lower the noise. BTW, my fan is actually on the roof which is probably the quietest option.

Just make sure it's for motors, and try it. Reducing noise will greatly reduce air flow. Ideally you want the fan like in the attic. That's what I will do eventually, just like my bath.

Greg