Alton Brown's "burger of the gods" is the best hamburger patty recipe around — and this is the upgraded 21st century version.
Prepare the meat grinder and bowls
When you're making ground meat, it's vital everything stays cold. When the meat gets warm, it tends to smear more easily (becoming a paste rather than a grind), and the fat may separate from the meat, which will leave your burgers dry and crumbly.
About an hour before you start grinding, put your grinder attachment (or the plates and any other parts that touch the meat) in the freezer along with two bowls (one to catch the meat, the other to hold ice water to keep the bowl cold while you're grinding). You'll want the larger of the two grinder plates. If you want a smaller grind, you'll have to grind it twice, first using the larger, then the smaller.
Trim and cube the chuck and sirloin
Meanwhile, trim as much of the fatty sinew as possible off both cuts of meat. It can get caught in the grinder, clogging it and making your meat smear. Make sure you put the cuts back in the refrigerator when you're not working with them to keep them cold.
Cube both cuts of meat into a size that will easily fit into your grinder. These 1-1/2-inch cubes were a good size for a KitchenAid attachment.
If you don't want to mess with this step, you can ask your butcher to trim and cut (and maybe even grind) the meat for you.
Put the cubes into a bowl, sprinkle them with salt and toss them together. Put the bowl back into the fridge while you put your grinder together. Don't forget about those cold bowls. Fill the larger of the two with a little ice and some water and fit the smaller one inside to keep it nice and cold while you grind. The nested bowl will catch your ground meat, so place it under the grinder plate.
Feed the meat into the grinder
Turn on the grinder and begin feeding the meat, a cube or two at a time, into the hopper using the pusher (not your fingers) to push it through. Alternate between sirloin and chuck to reduce how much you have to handle it to mix it later.
Keep an eye on the grind
It will start to feed from the blade end. Keep an eye out to make sure it's landing in the bowl and that nothing clogs. If there's a clog, stop the machine and remove it before continuing.
Check your grind
Take a look at your grind to make sure it seems well-mixed between chuck and sirloin. If there's any salt left in the bottom of the container the cubes were in, pour it into the catching bowl with the ground meat and gently toss it.
Cover it and put it back into the fridge for about half an hour (or until you need it). Remember: You want to keep the meat cold. If at any point during the following steps you have to walk away, the meat needs to go back in the fridge while you're gone.
Portion the ground meat
Weigh the meat into 5-ounce portions. That may seem like 1 ounce too few, but remember that you trimmed the meat.
Form the ground meat into balls
Gently (oh, so gently) form the meat into balls. If your hands tend to get hot, run them under cool water between balls. That will keep the meat from sticking to your hands (and keep the meat cool!).
Form the ground meat into patties
Form each ball into patties (again, gently) of about the same thickness — a little thicker than you think you need to. Use your knuckles to depress the center slightly on one side only. This indent or "cave" will prevent the patties from puffing up when you cook them. Puffy burgers still taste good, but they do cause issues when you're topping the burger.
Cook the ground meat patty
Unless you're grilling out, I recommend a preheated cast-iron skillet for cooking hamburgers (and any other meats you need a good sear on). Just turn your burner to medium-high heat for a couple of minutes. You shouldn't need any oil because of the fat in the patties.
Put the patties in the skillet (only a few at a time — you want to have room to flip) and don't touch them! Leave them on the first side for about 4 minutes (medium-rare). For medium, go 5 minutes. For medium-well, go 6 minutes.
Flip the ground meat patty
Once the patty is ready, it will release from the skillet (or grill) pretty easily. After the time is up on the first side, flip that bad boy. Cook it on the other side for the same amount of time, then pull it off. Don't flip it again or check it. Don't cut it open. Just believe. You don't have to believe in me. Believe in Alton. Believe in the beef. Believe in the tooth fairy if you need to.
Pull it off and let it rest for about 5 minutes.
If you really don't trust yourself (or your stove's version of what medium-high is), do one patty first. Call it a trial run. It's your excuse as the chef to try it before everyone else. After it rests, then you can cut it open and check the doneness (or use a thermometer). If you're satisfied, cook the rest the same way.
Top your burger
Now just assemble your burger as you see fit. If you're having a party, invite your guests to do so after the resting period is up. You don't want the burgers to get cold, because if you have to reheat them, you'll continue cooking them.