Trim the broccoli to bite sizes. Place them in a large microwave safe bowl with 2 tbsp water. Cover the bowl and microwave on high for 1.5 minute. Toss the florets and microwave for 1 additional minute. The florets should be in vibrant green, crisp, not completely cooked through with some bites to them. Rinse them in cold water and set aside to drain well.
Aromatics and garlic sauce:
Prepare the garlic and green onions and separate the white and green parts. Combine the sauce from coconut aminos to starch in a small bowl. Stir-well.
Prepare the shrimp:
Pat dry the shrimp with clean paper towels. Butterfly them with a small paring knife - make a shallow slice on the back of them shrimp down the middle, cutting almost but not all the way through to expose the vein. The butterfly step is optional but will help the shrimp cook evenly and more pleasing in presentation.
Sear the shrimp:
Preheat a large skillet or wok over medium heat until it feels hot, add 1.5 tbsp oil. Quickly place the shrimp one-by-one to the skillet and fry them in a single layer over medium-high heat about 2-3 minutes on the first side. Do not flip or move around the shrimp. Then, quickly flip them with a tong or chopsticks to fry the second side for about 1-2 minutes.
Keep your pan hot when searing the shrimp. You want to the outer is lightly browned and the inside is not completely cooked through. You should hear sizzling sound throughout. This way the shrimp will retain their juices without turning rubbery.
Scoop them out along with pan juice and scrape off any brown bits into a bowl and set aside to keep warm.
Sauteing:
Use the same pan, add the remaining oil. Add the garlic and white scallion parts with a pinch of salt and saute over medium heat for 5 seconds.
Add the blanched broccoli and season with 2 pinches of salt. Turn heat up to medium-high, keep stir frying and tossing for 30 seconds.
Return the shrimp to the pan. Stir the sauce again then pour it in. Keep tossing and scooping for 30 more seconds. The sauce should thicken.
Turn off heat. Transfer to a larger serving plate. Garnish with green scallion parts and drizzle with sesame oil. Serve warm.
Notes
To blanch the broccoli florets: Bring a large pot of water to boil. In the meantime, trim the broccoli to bite sizes. For stems, remove the outer tough part and dice to bite sizes. Rinse and set aside. Blanch the broccoli florets in hot boiling water for about 1.5 minutes. Drain and rinse with cold water. Set aside to drain well or use a clean kitchen towel to pat dry the florets. Note: If using pre-cut florets, blanch for 1 minute total.