Boil the pasta. Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente. Reserve at least 1/2 cup of pasta water, then drain and set aside.
Prep the sauce base. In a small bowl, whisk together honey, soy sauce, vinegar, lemon zest, and crushed red pepper flakes. Keep the lemon juice for the end so it tastes bright, not cooked down.
Season the chicken. Pat chicken dry and toss with a big pinch of salt and pepper. Dry chicken browns better and stays juicy.
Sear the chicken. Heat olive oil in a large skillet over medium-high.
Add chicken in a single layer and cook 3–5 minutes, stirring once or twice, until lightly browned and cooked through. Transfer to a plate.
Soften the veggies. In the same pan, add broccoli and bell pepper with a splash of broth. Cook 3–4 minutes until crisp-tender.
If the pan is dry, add another teaspoon of oil.
Sauté the garlic. Push the veggies to the edges. Add minced garlic to the center with a small drizzle of oil. Cook 30–45 seconds until fragrant. Don’t brown the garlic—it turns bitter.
Build the sauce. Pour in the honey-soy mixture and remaining broth.
Bring to a gentle simmer for 1–2 minutes so it thickens slightly.
Combine with chicken. Return chicken and any juices to the pan. Toss to coat. If the sauce feels tight, add a splash of reserved pasta water to loosen and make it glossy.
Add pasta and finish. Add cooked pasta and toss over low heat.
Stir in 1–2 teaspoons lemon juice to brighten. Taste and adjust salt, pepper, and heat. If you like, finish with a few drops of sesame oil for depth.
Garnish and serve. Top with chopped parsley or green onions and a sprinkle of sesame seeds.
Serve warm.