Boil a large pot of water and cook your noodles according to package instructions. Once done, drain and rinse under cold water to stop cooking and prevent sticking.
In a small bowl, combine soy sauce, garlic, coconut sugar, chili-garlic sauce, hoisin, and sesame oil. Taste and tweak balance if needed—more sugar, more heat, or more soy.
Heat the vegetable oil in your skillet or wok over medium-high heat. Add bell pepper and carrot first; cook, stirring, about 3 minutes until starting to soften. Then toss in broccoli and stir a couple more minutes until bright green and crisp-tender.
Add the drained noodles into the skillet with the veggies. Pour your sauce over, fold gently to coat everything evenly. Let it cook for another 2–3 minutes until heated through and the sauce slightly thickens.
Transfer to serving bowls, and sprinkle with green onions and toasted sesame seeds if using. Serve hot or at room temperature.