In a small bowl, combine soy sauce, sesame oil, hoisin sauce (if using), brown sugar, garlic, ginger, chicken broth, and red pepper, then set aside.
In another bowl, season shrimp with salt and pepper and mix with cornstarch until well coated.
In a large skillet over medium-high heat, heat 1 tablespoon oil and cook shrimp until golden-brown and slightly crispy, about 4 minutes per side; set aside.
Add remaining tablespoon oil, broccoli, and red pepper and cook until tender, about 2 minutes. Add cooked shrimp and sauce and simmer for 5 minutes until thickened, stirring often to coat.
Garnish with green onion and sesame seeds and serve over cooked rice.