What's the best way to drill an 11/32" hole there?
Drilling the hole is the EASY part.
Assuming you have a drill and a nice way to position the mixer, even on its face, then you have to go inside. Have you been inside? Have you found a spot where there's plenty of clearance? No circuit boards nearby? In a modern piece, real estate is usually a premium and vacant areas can be hard to come by.
If so, then the hole can be done several ways, but most probably, and i'm speaking generically here, by a step process.
Get a small bit. No more than 1/8". The reason being is that it's easy to see, easy to drill, and still closely control the location.
After marking your spot, drill through with that. If it's where you want it, then drill it out to 11/32". Done.
Just that easy? Hardly.
All that material that was once in the hole has to go somewhere. Metal people often call this "swarf". A little is stuck to the bit. Most is outside (or the side you drilled from). But SOME of it is on the inside. If the panel is plastic, it's probably not a big deal, but if the panel is metal, then those little metal bits can do many bad things. Also, if the plastic is conductive, it's a big deal. I'm sure you get the picture.
The answer is in prevention. No, there's no special way to work your drill to keep it from making a mess, the trick is to catch the mess as it happens.
One way is to have a vacuum cleaner running with the hose right there on the spot while you drill. This works very well, and it's served me many times successfully. It all sounds very industrial, too, with two motors going and all. Makes you sound like you know what you're doing.
Also, you can cover everything nearby and then cover that with something sticky, like upside down tape. That will nab those pesky chips, also. But then you have to lift it all out without spilling, which has vexed me once or twice. So run your vacuum on that, too.
First step, see if you CAN. See if your mixer will cooperate. Then drill baby drill ;-)
Dunno if any of that helps.
Ponder5