Prepare your broccoli, garlic, and ginger. Wash your shrimp under cold water and pat dry well.
In a medium pot, add all of the sauce ingredients and bring to a boil over medium heat. Reduce heat to low heat and let the sauce simmer about 20 mins (or until the rest of the dish is finished cooking). Cover with a lid and stir occasionally.
In a large pan, add olive oil over medium heat then add the shrimp. Cook them for about 3 minutes per side or until they are pink and then set aside.
Add the broccoli to the pan and 3 tbsp of water, garlic, ginger, and pepper. You can cover the pan with a lid to help the broccoli cook faster. Stir occasionally.
If the broccoli starts to stick to the pan, add in another tablespoon of water.
Cook until the broccoli is soft and then add the shrimp into the pan with the sauce. Cook for 4-5 more minutes so that the broccoli and shrimp can soak up the sauce.
Remove the pan from the heat, top with sesame seeds and scallions and ENJOY!