Heat gas or charcoal grill. In small bowl, mix mayonnaise, 1 tablespoon Sriracha sauce, the lime juice and 1/4 teaspoon soy sauce until well blended. Refrigerate until serving time.
In large bowl, mix beef, 2 tablespoons Sriracha sauce and 2 tablespoons soy sauce. Shape mixture into 4 patties, about 1/2 inch thick.
Place patties on grill over medium heat. Cover grill; cook 10 to 12 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Top each burger with 1 to 2 cheese slices. Cover; cook 1 minute longer or until cheese is melted.
Spread cut sides of buns with spicy mayonnaise. Place burgers on bun bottoms; top with jalapeños. Cover with bun tops.