In a large cast-iron skillet over medium-low heat, combine onion and 1 tablespoon butter. Heat and cook, stirring occasionally, 30-35 minutes or until onion is well caramelized. Set aside.

Meanwhile, heat oven to 350°F. Line a baking sheet with foil. Spread remaining 1 tablespoon butter on split sides of brioche buns; place buttered side-up on baking sheet. Bake 5-8 minutes until buns are lightly toasted.

Make the burgers: In a large bowl, mix ground beef with a few generous pinches of kosher salt. Divide beef into 12 equal-size balls. Place one ball on a cutting board. Press into a large, flat round, about 6 inches wide. Top with 4 pieces of cheese (1 slice cheese total). Take another ball of beef; press into a thin, 5-inch-wide round. Place on top of larger beef round; fold and seal edges of larger beef round up over smaller beef round to fully encase cheese within patty. Repeat with remaining beef and cheese to form 6 patties.

Heat grill or clean and dry cast-iron skillet over medium-high heat. Sprinkle tops of patties with salt. Grill or pan-fry patties on each side about 5-6 minutes, until deeply browned and an instant-read thermometer inserted in center of each patty reads 160°F (use caution to avoid cheese from spilling out of hole from thermometer; I inserted mine in the center, top-down). Transfer to a plate; let sit 5-10 minutes to allow cheese to cool slightly.

Meanwhile, assemble burgers. Spread cream cheese on tops and bottoms of buns, about 1 tablespoon for each whole bun. Top with burger patty, then 1 slice tomato, 2 slices bacon, a leaf of lettuce and a generous spoonful of caramelized onions.