Shape the burgers: In a large bowl, gently break up the ground beef, then divide the meat into 8 equal sized portions, each weighing 5 ounces. Form each portion into a patty, roughly 1/2 inch thick by 4 inches wide. Be careful not to overwork the meat – handle it as little as possible – but make sure the edges are well formed to hold the burger together on the grill. (This is where a burger press comes in handy.) Repeat until you have eight burgers. Sprinkle the salt and pepper over the burgers.
Set the grill to direct medium heat: Set up the grill for direct medium heat, with a section of the grill with no heat (for flareups). On my Weber gas grill, I preheat my grill for 15 minutes with all the burners on high, brush the grates clean with a grill brush, then turn half the burners down to medium, and the other half off.
Cook the burgers, onions, and peppers: Set the burgers, onions, and jalapeno peppers on the grill over direct medium heat. (On a gas grill, I keep the lid closed as much as possible while grilling.) Total cooking time is about 10 minutes. Grill the burgers, onions, and jalapenos until they are well browned on the bottom, about five minutes. Flip the burgers, onions, and jalapenos, and grill until the burgers are cooked through and browned on the bottom, about five more minutes. If the burgers cause a large flare up, move them to the no heat side of the grill grate for a few seconds to let the flames die down. It’s OK if the jalapenos blacken – you peel the burnt skin off before serving. During the last few minutes of grilling, put the buns on the grill until toasted on the bottom, about 1 minute. (Watch the buns carefully – they will go from toasted to burnt very quickly). Put the buns on a platter, add a slice of cheese on the bottom piece of each bun. Put a slice of onion on the cheese, then the burger on top of the onion. Let the burgers rest while you clean the jalapenos.
Clean the jalapenos, slice, and serve: Peel any burnt skin off of the jalapenos, trim off the stem end, then cut them lengthwise into quarters. Use a teaspoon to scrape the seeds off of the jalapenos. Top each burger with a spoonful of salsa and two jalapeno quarters. Add a slice of lettuce, put the bun on top, and serve.