Make the sauce: In a bowl, whisk together soy sauce, oyster sauce, honey, rice vinegar, broth, chili-garlic sauce, and cornstarch until smooth. Set aside.
Prep the shrimp and broccoli: Pat the shrimp dry with paper towels and season lightly with salt and pepper. Cut broccoli into bite-size florets.
Have garlic and ginger ready.
Heat the pan: Place a large skillet or wok over medium-high heat. Add 1 tablespoon oil and swirl to coat.
Sear the shrimp: Add shrimp in a single layer. Cook 1–2 minutes per side until just opaque and lightly golden.
Remove to a plate. Do not overcook.
Cook the broccoli: Add remaining 1 tablespoon oil to the pan. Toss in broccoli and a pinch of salt.
Stir-fry 2 minutes. Splash in 2 tablespoons water, cover for 1 minute to steam until crisp-tender.
Add aromatics: Uncover and add garlic and ginger. Stir-fry 30–45 seconds until fragrant.
Keep them moving so they don’t burn.
Sauce it up: Stir the sauce again (cornstarch settles), then pour it into the pan. Bring to a simmer and cook 1–2 minutes, stirring, until glossy and slightly thickened.
Finish with shrimp: Return shrimp and any juices to the pan. Toss to coat and warm through, 30–60 seconds.
Turn off heat and drizzle in sesame oil.
Serve: Top with green onions and sesame seeds. Serve over rice or noodles while hot.