If your squid is whole and uncleaned, pull the head and tentacles away from the body tube, remove the plastic-like quill from inside the tube, and peel off the thin outer membrane. Rinse well. Skip this step entirely if using pre-cleaned or frozen ring-cut squid.
Cut the tube open flat and score the inside surface in a shallow crosshatch pattern, cuts about 5 mm / 1/4 in apart, without cutting all the way through. Skip this step if using pre-cut rings.
Cut the scored tube into bite-size pieces, roughly 4 cm / 1 1/2 in squares; leave rings as they are if using pre-cut squid.
Whisk the gochujang, gochugaru, soy sauce, sugar, garlic, ginger, and sesame oil together until smooth.
Heat the neutral oil in a wide pan or wok over high heat until shimmering.
Add the onion and carrot and stir-fry 2 minutes, until the onion softens at the edges.
Add the squid and the sauce together, all at once, and toss constantly over high heat.
Cook for 90 seconds to 2 minutes only. Watch for the scored pieces curling into a tight spiral shape and the squid turning fully opaque — that's your signal it's done. Squid overcooks in seconds, so pull it the moment it curls.
Add the cabbage and scallions in the final 30 seconds, tossing just until they wilt slightly.
Scatter sesame seeds over the top and serve immediately with rice.