Toss the shrimp with 1 teaspoon of the cornstarch, a pinch of salt, a dash of white (or black) pepper, and the sesame oil in a medium bowl; set aside to marinate while you prepare the vegetables.
Bring about 1 cup of water to a boil in the wok or sauté pan over medium-high heat. Add the broccoli, cover, and blanch for 1 minute, shaking the pan halfway through; the broccoli should be bright green and slightly crisp. Drain and set aside, then wipe the pan dry.
In a small bowl, whisk the remaining 1 teaspoon cornstarch with the soy sauce and oyster sauce until smooth; set aside.
Heat 1 tablespoon of oil in the pan over medium-high heat. Add the marinated shrimp and stir-fry for about 2 minutes, until pink and just cooked through. Remove the shrimp and set aside.
Wipe the pan clean, then heat the remaining 1 tablespoon oil over high heat. Add the sliced onion and snow peas and stir-fry until fragrant, about 1 minute. Add the minced garlic and stir for 30 seconds more.
Pour in the chicken stock and bring to a boil, then stir in the soy-oyster-cornstarch mixture and cook until the sauce thickens, about 30 seconds.
Add the halved baby corn and stir-fry for 1 minute. Return the reserved shrimp and the blanched broccoli to the pan and stir constantly for 1 minute, until everything is heated through and coated with sauce. Serve immediately.
