From Serious Eats, my second most utilized food reference: http://www.seriouseats.com/recipes/2010/08/grilling-honey-chiptole-wings-recipe.html
And for the burgers, if you don't have a meat grinder, get one! They're cheap ($15? $20?) and the only trick is you gotta put everything in the freezer before it touches the meat. Warm grinder = meat paste = bad burger. For the meat, just rough cut a pound of chuck and a pound of de-boned short ribs into 1" cubes and feed it into the grinder with a few squares of beef tallow (beef fat, you can get it for free at most butchers'). Take the beef and shape it into patties, and then you can do two things:
1. (expensive option) Buy one of these: http://www.auberins.com/index.php?main_page=product_info&cPath=13&products_id=42
and one of these: http://www.amazon.com/o/ASIN/B000AANXDG?tag=betteraddons-20
and seal (but don't crush seal!) two burgers per package. Drop them in a rice cooker hooked up to the PID at around 54.5 degrees C for at least an hour, two or three or all day is fine too, just don't go lower than 54.5 ish otherwise e. coli will get an invitation to party. When they're done, take them out of the package (carefully! they're fragile right now) and put them onto either a very very very hot grill or a very very very hot cast iron pan. There Will Be Smoke. You don't have to worry about letting them rest because they've already rested for a few hours in the cooker. Eat 'em!
2. (inexpensive option) Buy one of these: http://www.amazon.com/o/ASIN/B000G64I1A?tag=betteraddons-20
and fill it up with ~58 degree C water (you'll need a thermometer of course). Buy some of these: http://www.amazon.com/o/ASIN/B002GJO6R6?tag=betteraddons-20
and put one patty in per bag. Fill up your sink with water and seal the bag almost all the way, then dip it slowly in the water with the patty centered in the bag. As the bag goes into the water, it'll push the air out, forming a quasi-vacuum. At the very last moment, close the last bit of the bag. Drop them in the cooler and close the lid, keeping an eye on the temp every now and then. Put into hot skillet or grill as above, OR, use this:
My Super Secret Steak Searing Success Scheme (stolen from Alton Brown):
Take a chimney starter and load it with about a pound or so of lump (NOT briquettes!) hardwood charcoal. Let it get really, really hot. Take a grill grate and put one hamburger at a time on the grate, and then put the chimney on top. Let it sizzle for ~30 seconds and then flip. Perfect char! You can also do this with steaks: 90 seconds per side, then move the grate to the top of the chimney starter and put the steak on for a minute, covering with a metal bowl. Flip, cook another minute, and then for GOD'S SAKE LET IT REST, DO NOT CUT INTO IT IMMEDIATELY. 5-10 minutes should be enough. Voila, awesome steak.
Hey, that's my longest post ever!