In a skillet over medium heat, add olive oil and sauté the sliced onions until they are caramelized, about 10-15 minutes. Add the diced jalapeños and cook for an additional 2-3 minutes. Remove from heat and set aside.
In a large bowl, combine the ground beef, garlic powder, smoked paprika, salt, and pepper. Mix gently until just combined; do not overwork the meat.
Divide the beef mixture into 4 equal portions and shape them into loose balls. Do not flatten them yet.
Heat a griddle or large skillet over high heat. Once hot, place the meat balls on the griddle and use a spatula to smash them down into thin patties. Cook for about 3-4 minutes until a crust forms on the bottom.
Flip the patties and immediately place a slice of cheddar cheese on each one. Cook for an additional 2-3 minutes until the cheese is melted and the burgers are cooked to your desired doneness.
Toast the hamburger buns on the griddle for 1-2 minutes until golden brown.
Assemble the burgers by placing the cheesy patties on the bottom half of each bun, topping with the jalapeño onion mixture, and adding lettuce, tomato, and any additional condiments. Place the top half of the bun on each burger.