Combine the jalapeno, onion, garlic, olive oil, kosher salt, and Italian seasoning in a medium mixing bowl. Add the ground beef and combine using your hands.
Divide the burger meat into four balls. One at a time, divide a ball in half and flatten both halves. Place a few slices of cheese on one of the halves, leaving a border about 1/4 inch thick. Top with the other half and pinch the edges of the patties together to seal. Repeat with remaining three balls.