In a large mixing bowl, gently combine the ground beef with freshly pressed garlic, grated ginger, sesame oil, soy sauce, and black pepper. Mix with hands until just combined; avoid overworking the meat to keep it tender. Form into four 6-ounce patties with a small indentation in the center. Cover and refrigerate for at least 1 hour.

Preheat a cast-iron skillet over medium-high heat and add a drizzle of oil. Place the patties in the skillet and sear for about 3-4 minutes on each side until golden brown crust forms. Cook until they reach an internal temperature of 160°F. Remove from skillet and let rest for 5 minutes.

Warm the Korean BBQ sauce in a small saucepan over low heat. Place each patty back in the skillet and brush generously with the warm sauce before assembling.

Slice the brioche hamburger buns in half and toast them in the skillet cut side down until golden brown. Remove from skillet.

Spread chili garlic mayo on the bottom half of each toasted bun. Place a glazed patty on top, add a scoop of kimchi slaw, and finish with the top half of the bun.

Serve immediately with sides like sweet potato fries or potato chips.