My favorte burger in Denver is the 'Hot Hamburger' at Pete's Kitchen at Colfax and Race St's.
The hot hamburger is actually from another Greek diner, Pete's Coney Island, that used to be downtown on 15th. St. and was torn down to make way for the convention center.
What the hot hamburger is, is take two slices of white bread and place them on top of each other on a large oval plate. Then, place a hamburger patty on top of the slices of bread. Next, place a bunch of hashbrowns next to the open face burger. And finally, cover the whole thing with chili con carne.
It was better at the Coney Island, because the chili was better, but I still stop in for one at Pete's just for old times sake. The breakfast burrito is not to be missed, also.