If needed, peel and devein the shrimp, removing any remaining shells. Rinse the shrimp with cold running water, drain, and pat dry with paper towels. Then transfer to a large bowl. Add all the shrimp marinade ingredients and mix well to coat evenly. Set aside for 10 minutes.
In a small bowl, combine all the stir-fry sauce ingredients and mix well until the sugar fully dissolves. Set aside.
Fill a large pan halfway with water and bring to a boil over medium-high heat. Add the broccoli florets and blanch for about 2-3 minutes or until vibrant green and crisp-tender. Drain well in a colander and set aside.
Dry the pan and heat 1 tablespoon (15 ml) vegetable oil over medium heat. Using tongs, transfer the shrimp individually into the pan in a single layer, allowing excess marinade to drip off. Cook for about 1-1.5 minutes total, flipping halfway through, until the shrimp turn pink on the outside but remain slightly translucent in the center. Remove and set aside.
Reduce the heat to low and add the remaining vegetable oil, garlic, and ginger. Stir-fry for about 10 seconds until fragrant.
Stir the prepared sauce again to redistribute the cornstarch, then pour it into the pan. Increase the heat to medium-high and simmer until thickened and glossy, about 2-4 minutes.
Return the shrimp and broccoli to the pan. Toss everything in the sauce until evenly coated, the broccoli is heated through, and the shrimp are opaque and reach an internal temperature of 145°F. Remove from the heat and serve immediately.