Mix 2 tablespoons sesame oil, soy sauce, honey, salt, pepper, and garlic together and pour over shrimp. Refrigerate for 1 hour.
Heat remaining 1 tablespoon sesame oil over medium-low heat in a pan. Remove shrimp from marinade, add to the pan, and cook 2 minutes. Add broccoli florets and cook 2 minutes longer, or until shrimp is cooked through.
In a small pan or the microwave, reheat frozen (already prepared) jasmine rice. Serve shrimp and sauce over rice.
To prepare and freeze:
Mix 2 tablespoons sesame oil, soy sauce, honey, salt, pepper, and garlic together in one container. Place shrimp in a separate container. Place broccoli florets in another container. Freeze all containers for up to 3 months.
To cook from frozen:
Thaw marinade, shrimp, and broccoli. Add shrimp to marinade. Let sit for an hour in the fridge and then follow cooking instructions.