How to Make It
In a blender, combine the fresh jalapeños with 1/2 cup of the cilantro, the garlic, lime juice, water, 1/2 teaspoon of the ground cumin and a generous pinch of salt. Puree the jalapeño-cumin sauce until smooth.
In a medium bowl, lightly knead the sirloin with the Pepper Jack cheese, the remaining 3 tablespoons of cilantro and 1/2 teaspoon of cumin. Loosely shape into 4 patties about 3/4 inch thick; tuck any large pieces of cheese into the burgers. Season very generously with salt and pepper and transfer to a plate lined with plastic wrap. Brush the cut sides of the buns with olive oil.
Light a grill. When the fire is medium hot, brush the grate with olive oil. Grill the cheeseburgers for about 10 minutes, turning once, for medium meat. Move the cheeseburgers away from the heat and grill the cut sides of the buns until they are toasted, about 1 minute.
Spread a thin layer of mayonnaise on the cut sides of the buns. Set the cheeseburgers on the bottom halves and top with the lettuce, tomato and pickled jalapeños. Spoon some of the jalapeño sauce on the burgers, top with the buns and serve right away, passing the remaining sauce on the side.