I set mine on the counter (can't submerge ours, either), with the run-off over the edge of the sink. While it's still very warm (but unplugged!) I'll pour hot soapy water over it, and it just drains all the gunky stuff down into the sink. Once the worst of it's gone, a quick wipe down with a paper towel will do the trick.

If you're a disinfecting fanatic, after rinsing with the hot soapy wather, give it a quick wipe with a Clorox wipe, then rinse again and wipe dry with the paper towel