In a mixing bow, mix Korean chili paste, chili flakes, soy sauce, sugar, garlic, pepper, and sesame oil until it becomes smooth paste.
Add the squid slices and toss well together to incorporate with the sauce. Set aside.
Heat oil in a skillet over med-high heat. Add the onion and carrot and saute until just soft, about 2-3 minutes. Add the squid mixture to the skillet and stir-fry quickly until the squid is cooked enough, about 2-3 minutes. Do not overcook the squid. It will get tough.
Remove the skillet from the heat and sprinkle with green onion and sesame seeds. Serve hot over rice.