In a large pot with salted boiling water, cook the spaghetti according to package directions.
Add in the broccoli florets the last 2-3 minutes of cooking and let them cook together with the pasta until tender. Drain and set aside.
In a small bowl whisk soy sauce/coconut amino, orange juice, honey, hoisin sauce, sesame oil, ginger, and chili flakes.
Heat 1 tablespoon of oil in a large skillet over medium-high heat. Add in shrimp, garlic, a pinch of salt and pepper.
Cook for 2-3 minutes, then stir in carrots and bell pepper and cook for a minute more, or until everything is heated through.
Add in the cooked spaghetti and broccoli, then pour the sauce over and toss to combine.
Garnish with green onions and sesame seeds. Enjoy!