Gochujang does double duty here: it’s used to flavor the pork bulgogi-inspired patties, along with plenty of garlic, and tossed with cabbage and carrots. Grilled julienned bell peppers and fresh lime juice complete the umami-packed burger topping.
Whisk together the gochujang paste, olive oil, vinegar, sesame seeds, sesame oil, sugar and garlic in a large bowl; transfer half of the mixture to a medium bowl and set aside until ready to use.
Add the pork, onions, 1 1/2 teaspoons salt and 1/2 teaspoon pepper to the large bowl with half of the gochujang mixture. Using 2 forks, begin “pulling” the ground pork apart as if you were shredding pulled pork, breaking up the clumps and incorporating the ingredients together without compacting the meat into a dense mass. Continue to pull the meat apart until thoroughly mixed and no clumps of onion or pork remain and all of the gochujang mixture has been absorbed.
Lightly oil your hands. Working one at a time, divide the pork mixture into 4 equal portions; roll gently between your hands into balls. Arrange on a rimmed baking sheet and flatten to patties about 1 inch thick.
Toss the cabbage, carrots and scallions in the medium bowl with the reserved gochujang mixture until completely coated; season with salt and pepper. Let sit until ready to serve.
Prepare a grill or large grill pan for medium-high heat. Clean and oil the grill grates.
Grill the buns until toasted on both sides, about 1 minute per side. Transfer to a baking sheet. Brush the patties with oil and grill until lightly charred on both sides, about 4 minutes per side. Transfer the burgers to the buns and let sit 5 minutes.
Meanwhile, grill the peppers until charred in spots on both sides, about 5 minutes per side. Transfer to a cutting board and slice; season with salt and pepper directly on the board.
Liberally spread mayonnaise on the top buns. To serve, top the burgers with the tomato slices, grilled peppers, gochujang slaw, a squeeze of lime and the top buns.