Add one tablespoon of vegetable oil to a large skillet over medium heat and add the shrimp in even layer to the pan.
Let them fry, untouched for 2 minutes, then flip then over and let them cook again for another 2 minutes.
Remove them from the pan and set aside.
Wipe out the pan then add the broccoli and 2 cups of water to the pan.
Cover and let it simmer over medium heat for 2 minutes then drain out the water and set the broccoli aside.
Add the pan back to the stove over low-medium heat and add the remaining olive oil, garlic and ginger and cook for about 2 minutes, or until they become fragrant.
In a small bowl, combine the soy sauce, lime juice, honey, cornstarch and rice wine vinegar and stir to combine.
Add it to the pan and stir the entire time as the sauce thickens for about 2 minutes. Add a bit of soy sauce if it’s too thick for your liking.
Add the shrimp and broccoli back to the pan and stir to combine.
Let it simmer again for another 2-3 minutes, or until the broccoli reaches your desired doneness and the sauce thickens to your liking.
Serve over rice or noodles with freshly chopped green onions and toasted sesame seeds. Leftovers can be stored in the refrigerator up to 4 days.
To Make this a Freezer Meal: If you're planning to make and freeze, you don't need to do any cooking beforehand. Just whisk your sauce ingredients together then stir in the shrimp and broccoli. Now you can freeze it for up to one month. To cook from frozen, just heat up your oil in a large skillet over medium-high heat and stir fry everything for about 6-8 minutes.