Is it "Belgian" waffle or "Belgium" waffle?

This is a question that my spouse and I have have talked about before, most recently at dinner tonight.

We were having dinner at the Capitol Cafe/Grecian Inn Restaurant, located on Capitol Drive, slightly west of the intersection of Capitol and Lilly Road.  For those who don't know, the building that housed the Grecian Inn is now home to two restaurants, the Capitol Cafe and Pancake House on the main level and the Grecian Inn on the lower level (formerly the pub).  It's my understanding that both businesses are owned by members of the same family.

I have been a loyal fan of the Grecian Inn for years, dating back to when it was a cozy little place on North Avenue.  (Speaking of dating, it was my first boyfriend, who was half-Greek, who introduced me to the restaurant.)  I haven't been to the "new" Grecian Inn yet, but from looking at the menu, the lower level is now devoted exclusively to Greek dishes. I particularly noticed an expanded seafood section. 

On the upper level, the Capitol Cafe and Pancake House hasn't changed layout wise.  On the menu, you'll probably still see your favorite specials -- like the Friday Fish Fry-- and even a few of the popular Greek entrees like the roast lamb sandwich or the gyro sandwich.

As the name implies, you're also still able to order breakfast anytime, and the breakfast menu is bigger and better than before.  There are all kinds of pancakes and crepes, different kinds of eggs benedict, an expanded kids menu, and of course waffles, which brings us back to our question.

On the menu, it said "Belgium" waffle, which incidentally is what I ended up ordering, but I've also seen it as "Belgian" waffle in other restaurants. 

I think the latter is correct.  My argument is that "Belgium" is not an adjective.

Maybe we should just call it the Brussels waffle?