First, make the green onion salad. Add the rice vinegar, honey, grated ginger, and salt into a bowl and whisk. Add the green onions and toss with the dressing. Top with sesame seeds and place in the refrigerator for later
Next, make the pork noodle sauce. Add the gochujang, tomato paste, rice vinegar, soy sauce, fish sauce, honey, and ginger to a bowl and whisk the ingredients together until combined. Drizzle 1 tablespoon of sesame oil into the sauce while whisking constantly until the mixture is homogeneous. Set aside.
Heat a large skillet over medium/high heat and add the ground pork to the pan. Season the pork with ½ teaspoon of salt. Break the pork up into small pieces and cook it until it’s almost cooked through (about 5 minutes) but still has some pink. Use a slotted spoon to remove the ground pork from the pan and transfer it into a separate bowl. Leave the drippings in the pan (there should be about 1-2 tablespoons of drippings).
Add 1 tablespoon of sesame oil to the pan and turn the heat down to medium heat. Add the white parts of the green onion to the pan and add ¼ teaspoon of salt to the onions. Saute the onions for 2-3 minutes and then add the minced garlic and saute for 1 additional minute.
Next, add the minced carrots and the rest of the salt to the skillet and mix. Saute them for 1 minute before adding the ground pork back into the pan. Toss all of the ingredients together.
Pour the gochujang sauce over the pork and other ingredients and mix until combined. Take the pan off of the heat and set it aside while preparing the noodles.
Bring a large pot of salted water to a boil and then add the noodles. Cook the noodles until they are just al dente (so they have a bit of bite to them). Remove 2 cups of starchy water from the pot before straining the noodles.
Place the skillet back on the stove and heat over medium heat. Add 1⁄2 cup of the starchy pasta water to the skillet and mix until combined. Bring the sauce to a gentle simmer and add another ½ cup of the starchy water to the skillet. Let the sauce simmer for 1-2 minutes or until it reaches your desired thickness.
Add the warm noodles to the skillet and toss with the sauce.
Sprinkle the noodles with sesame seeds and serve immediately topped with the green onion salad.