Pat the thawed large shrimp dry with paper towels, then place them in a medium bowl. Sprinkle with cornstarch and toss gently until each shrimp is lightly coated. Set aside.
In a separate small bowl, whisk together the soy sauce, oyster sauce, rice vinegar, sesame oil, and brown sugar until the sugar is fully dissolved and the sauce is well combined. This is your versatile stir-fry sauce.
Mince the garlic and grate the fresh ginger. Slice the green onions, separating the white and light green parts from the dark green tops. Dice the red bell pepper and thinly slice the carrots.
Heat canola oil in a large wok or skillet over high heat until shimmering. Add broccoli florets and carrots and stir-fry for 3-4 minutes until slightly tender-crisp. Add red bell pepper and the white/light green parts of the green onions, and continue to stir-fry for another 1-2 minutes.
Push the cooked vegetables to one side of the wok. Add the minced garlic and grated ginger to the empty side and stir-fry for 30 seconds until fragrant.
Add the cornstarch-coated shrimp to the wok along with the aromatics. Spread the shrimp in a single layer if possible and cook for 1-2 minutes per side until pink and opaque.
Pour the prepared stir-fry sauce over the shrimp and vegetables. Toss everything gently to ensure all ingredients are evenly coated. Cook for 1-2 minutes, stirring constantly, until the sauce thickens and coats the shrimp and vegetables beautifully.
Remove the wok from heat. Stir in the dark green tops of the green onions. Transfer the Shrimp Stir Fry to serving bowls. Serve immediately, ideally over steamed rice or noodles.