In a small bowl, whisk together the soy sauce, oyster sauce (if using), water or broth, and cornstarch until smooth. This will be your quick stir-fry sauce. Set aside.
Pat the chicken slices dry with a paper towel and season lightly with a pinch of salt. This helps the chicken brown nicely when it hits the pan.
Heat a large wok or skillet over medium-high heat and add the neutral oil. When the oil shimmers, add the chicken in a single layer and sear for 1–2 minutes per side until just cooked through. Remove the chicken to a plate and set aside.
In the same pan, add a bit more oil if needed. Add the garlic and ginger, sautéing for about 30 seconds until fragrant. Be careful not to burn them.
Add the mushrooms and carrot to the pan. Stir-fry for 2–3 minutes, until the mushrooms begin to soften and release their juices.
Pour in the prepared sauce and bring to a light simmer. Return the chicken to the pan and toss to coat. Stir-fry for another 2–3 minutes, until the sauce thickens and coats the ingredients.
Add the snow peas and stir-fry for 1–2 minutes more, until they are bright green and just tender-crisp. If the sauce needs a touch more looseness, add a splash of water or broth.
Finish with a drizzle of sesame oil (if using) and taste for seasoning. If you like, finish with sliced scallions for a fresh, crisp note.
Serve immediately over steamed rice or with noodles, and enjoy the bright flavors and satisfying textures right away.