Cook the noodles according to package instructions. Drain and set aside, reserving a little pasta water.
In a small bowl, whisk together the gochujang, soy sauce, sesame oil, honey, minced garlic, and grated ginger until well combined.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the sliced bell peppers, shredded carrots, and snap peas. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the cooked noodles to the skillet along with the gochujang sauce. Toss everything together, adding a splash of reserved pasta water if needed to loosen the sauce. Cook for an additional 2-3 minutes until heated through.
Remove from heat and stir in the sliced green onions. Serve hot, garnished with sesame seeds if desired.