Pat the shrimp and chicken pieces dry with paper towels. In a bowl combine 1 tsp salt and 1/2 tsp black pepper. Sprinkle seasoning evenly over the chicken pieces and shrimp. Toss to coat. Sprinkle 2 tablespoons cornstarch over the proteins and toss until lightly and evenly coated; the cornstarch helps the sauce cling and gives a slight velvety texture.

Sear proteins

Heat 1 tablespoon neutral oil in a large heavy skillet or wok over medium-high heat until shimmering. Add the chicken in a single layer (do in batches if necessary) and sear for 3–4 minutes, stirring occasionally, until just cooked through and lightly browned. Transfer chicken to a plate. Add another 1 tablespoon oil and when hot add shrimp. Cook shrimp 1–2 minutes per side until pink and just opaque. Remove shrimp to the same plate with chicken. Leave any fond in the pan.

Make Brown Sauce

Combine sauce ingredients

While proteins cook, whisk together 1/4 cup soy sauce, 2 tablespoons oyster sauce, 1 teaspoon dark soy sauce (if using), 1 cup chicken stock, 1 tablespoon brown sugar, 2 tablespoons rice wine or dry sherry, and 1 teaspoon sesame oil in a measuring cup or small bowl until the sugar dissolves.

Start aromatics

With the pan over medium heat and any browned bits present, add the white part of the scallions, 1 tablespoon minced ginger, and 3 cloves minced garlic. Stir-fry for about 30–45 seconds until fragrant, being careful not to burn the garlic.

Add vegetables

Add the red bell pepper strips and snap peas. Stir-fry 1–2 minutes so they stay crisp-tender.

Add sauce and simmer

Pour the prepared brown sauce into the pan, scraping the bottom to lift browned bits. Bring to a gentle boil, then reduce heat and simmer 2–3 minutes to meld flavors.

Thicken sauce

In a small bowl whisk 1 tablespoon cornstarch with 2 tablespoons cold water until smooth to make a slurry. Slowly pour the slurry into the simmering sauce while stirring. Continue to cook for 1–2 minutes until the sauce thickens to a glossy coat that clings to a spoon. If too thick, add up to 2–3 tablespoons water or stock to adjust consistency.

Finish & Serve

Return proteins to pan

Return the seared chicken and shrimp to the pan with the sauce and vegetables. Toss gently to coat and cook together for 1 minute to reheat and finish cooking the proteins. Taste and adjust seasoning with a pinch of salt or a splash more soy if needed.

Add scallion greens and garnish

Stir in the sliced green parts of the scallions, drizzle 1/2 teaspoon sesame oil if desired, and remove from heat. Sprinkle toasted sesame seeds and chopped cilantro or extra scallion greens over the top and finish with a light crack of black pepper.

Serve

Serve immediately over steamed rice or noodles so the sauce can be spooned over. Leftovers keep refrigerated in an airtight container for up to 2 days; reheat gently to avoid overcooking shrimp.