How to Make It
Heat broiler to high. Place jalapeños cut side down on a baking sheet lined with aluminum foil. Coat tops with cooking spray. Broil on middle rack of oven until just tender, 5 to 6 minutes. Cool slightly. Coarsely chop. Stir together chopped jalapeños, Cheddar, cream cheese, cayenne, and 1 teaspoon of the salt until smooth.
Place beef, garlic powder, onion powder, pepper, and remaining 1 1/2 teaspoons salt in a large bowl. Using your hands, combine thoroughly. Divide into 4 (6-ounce) balls. Flatten each ball into a 6-inch circle. Place 2 tablespoons of the cheese mixture in center of each burger leaving a 1-inch rim. Carefully fold edges of meat over to cover filling, and seal; flatten into 3/4-inch thick patties. Chill 15 minutes.
Heat oil in a nonstick skillet over medium-high. Cook burgers to desired degree of doneness, about 3 minutes per side for medium. Transfer to a paper towel-lined plate.
Spread 1 tablespoon mayonnaise on bottom and top halves of buns. Top bottom bun with a patty, tomato slice, onion, and pickled jalapeño, if desired. Top with top halves of buns.