Turn all grill burners to high and close lid to preheat.
For the spice rub: Mix 2 T. brown sugar, paprika, salt, black pepper and cayenne in a small bowl and set aside.
For the glaze: Stir 2 T. brown sugar, ketchup, vinegar, beer (take from your beer cans) and hot sauce in a bowl; add 1 T. spice rub; set aside.
Pour out about 1/2 cup or so from each can of beer. Using a church key can opener, punch holes in the top of the can to completely "open" the top; this will allow maximum steam to escape. Add 2 crumbled bay leaves to each can.
Loosen the skin on the chicken breasts and thighs of the chicken by sliding your fingers between the skin and the meat. Massage the spice mixture on the skin, under the skin, and inside the cavity. Using a skewer, poke the skin all over to render as much fat as possible while cooking.
Turn off all but primary grill burners, leaving main burner(s) on high (for my grill, I leave two burners on, but this will depend on how many burners your grill has -- mine has three. The temperature inside your grill should stay around 375). Place chickens on cans; place on cool part of grill, using drumsticks to stabilize them. Cover and grill until skin is very well browned and very crisp, 40 to 60 minutes. Brush with ketchup glaze and grill, covered, until thigh meat registers 170 degrees on instant-read thermometer, about 20 minutes longer.
Transfer chickens to cutting board and let rest for 10 minutes.