Bring a large pot of salted water to a boil. Cook the spaghetti according to package directions until al dente, usually 8-10 minutes. Drain and rinse with cold water to prevent sticking.

While the pasta cooks, prepare your sauce by whisking together soy sauce, teriyaki sauce, honey, and 2 tablespoons of water in a small bowl. Set aside.

Heat 2 tablespoons of vegetable oil in a large wok or skillet over high heat. Add carrots and stir-fry for 2 minutes. Add bell pepper, snow peas, and broccoli, cooking for another 3-4 minutes until vegetables are crisp-tender.

Push vegetables to the side of the pan and add the remaining tablespoon of oil. Add minced garlic and grated ginger, cooking for 30 seconds until fragrant.

Add the cooked spaghetti to the wok along with the prepared sauce. Toss everything together using tongs, ensuring the noodles and vegetables are evenly coated with sauce.

Cook for an additional 2-3 minutes, tossing frequently, until everything is heated through and the sauce has slightly thickened.

Remove from heat and garnish with sliced green onions and sesame seeds if desired. Serve immediately.