Pat the shrimp dry and season lightly with black pepper. Steam or blanch the broccoli for 2 to 3 minutes, then drain thoroughly.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Sear the shrimp for 1 to 2 minutes per side, just until pink. Transfer to a plate.
Reduce the heat to medium. Add the remaining butter and garlic, stirring for 30 seconds. Add the honey, soy sauce, lemon juice, and red pepper flakes.
Stir in the cornstarch slurry and simmer until glossy. Return the shrimp and broccoli, tossing for 1 minute until evenly coated. Serve immediately.