In a small bowl, combine the oyster sauce, soy sauce, and cilantro. Set aside.
Pat the shrimp with paper towels until they are dry. In a medium bowl, add the shrimp and cornstarch and toss to coat.
In a wok or large skillet, heat half the extra-virgin olive oil and swirl to coat the bottom of the skillet.
When the oil is very hot, add the shrimp in a single layer and cook partially until one side is seared brown, about 1 minute. Flip and sear the other side of each shrimp, about 1 more minute. They don’t need to be cooked all the way through yet. Remove them to a plate or bowl and set aside.
Turn the heat down to medium and let the skillet cool off a bit to prevent the aromatics from burning. Add the remaining olive oil and add the green onions, garlic, and ginger to the skillet and saute for a minute until fragrant.
Pour in the garlic ginger sauce mixture and add the shrimp back into the skillet. Saute for another minute until the shrimp is fully cooked.
Add the sugar snap peas and broccoli and saute for about 3 to 5 minutes.