In a bowl, combine the peeled and deveined shrimp with Shaoxing wine, salt, white pepper, and cornstarch. Mix well to ensure the shrimp are evenly coated. Allow them to marinate for about 15 minutes.

In a separate bowl, whisk together the chicken stock, oyster sauce, soy sauces, sugar, and additional cornstarch until well combined. Set it aside for later use.

Bring a small amount of water to a boil in a skillet. Add fresh broccoli florets, cover, and steam for about 1 minute. Transfer the steamed broccoli to a plate and set it aside.

In the same skillet, heat peanut oil over medium-high heat until it shimmers. Carefully add marinated shrimp in a single layer, cooking for about 1 minute until they are golden on the bottom. Flip each shrimp to cook the other side, allowing another minute for them to turn opaque and perfectly cooked.

Once the shrimp are done, toss in the minced garlic and ginger. Sauté for about 30 seconds, stirring frequently until fragrant and golden.

Stir the prepared sauce to ensure the cornstarch is well dissolved, then pour it into the skillet with the shrimp. Gently stir in the steamed broccoli, allowing everything to meld together. Cook for an additional 1-2 minutes or until the sauce has thickened.

Transfer the Shrimp and Broccoli onto a serving plate. Serve hot over a bed of steamed rice or alongside your favorite side salad.