What's the easiest way to clean a waffle maker that doesn't come apart

The first thing you should do is use lots of Pam cooking spray before you add the batter each time. I have a brush that is made to clean my Losge cast iron that works perfectly well this. You can ick one up for only a few dollars.

My honest opinion? Throw it away. If you must have waffles get a non-stick or one that comes apart. I can't think of anything any more infuriating that cleaning one of those things. If you still have your sanity after getting it clean, spray the heck out of it prior to the next use. Me? That's why I stick with pancakes in a non stick skillet.