Prepare the green onion salad by mixing rice vinegar, honey, grated ginger, and salt in a bowl. Toss in the green onions and sprinkle with sesame seeds. Chill in the refrigerator.
In another bowl, whisk together gochujang, tomato paste, rice vinegar, soy sauce, fish sauce, honey, and ginger for the pork noodle sauce. Drizzle 1 tablespoon of sesame oil into the mixture.
Cook ground pork in a skillet until almost cooked through. Remove pork and keep drippings.
Saute white parts of green onion, garlic, and carrots in sesame oil. Add pork back to the skillet and pour in the gochujang sauce. Mix well and set aside.
Cook noodles until al dente. Reserve starchy water.
Add starchy water to the skillet, simmer the sauce, and toss in the noodles.
Serve noodles topped with sesame seeds and the chilled green onion salad.