Preheat the oven to 400°F. Line a baking sheet with foil and set a wire rack over it. Cut the lamb rack into about 8 individual chops and season both sides with all-purpose seasoning.

Whisk the ginger, garlic, brown sugar, hoisin, gochujang, soy sauce, and vinegar together. Simmer gently in a small saucepan, stirring, until glossy and lightly syrupy. Reserve clean sauce for serving before brushing the meat, if desired.

Heat a thin layer of avocado or olive oil in a skillet. Sear the chops in batches for about 90 seconds to 2 minutes per side, until browned. Do not crowd the pan.

Transfer the chops to the prepared wire rack and brush with the glaze. Bake for about 10 minutes, checking early with an instant-read thermometer.

Cook the lamb to at least 145°F in the thickest part, away from the bone. Let rest at least 3 minutes before serving.