Place the chicken into the freezer for 10-15 minutes to make it easier to thinly slice.
While the chicken is in the freezer, whisk together 1 large egg white, 1 tablespoon low sodium soy sauce, and 1 tablespoon cornstarch in a medium mixing bowl until the cornstarch is dissolved.
Remove the chicken from the freezer and thinly slice the chicken against the grain into very thin slices. Place the chicken slices into the cornstarch mixture and toss to coat. Cover and refrigerate for 10 minutes or up to 1 hour.
While the chicken is marinating, prepare the sauce by whisking together ½ cup low-sodium chicken broth, ¼ cup Mirin, 1 tablespoon oyster sauce, 1 teaspoon toasted sesame oil, 2 cloves garlic (minced), 1 teaspoon freshly grated ginger, 1 teaspoon brown sugar, 1 tablespoon low sodium soy sauce, and 1 tablespoon cornstarch in a small mixing bowl or glass measuring cup until the cornstarch has dissolved. Set aside until needed.
After the chicken has marinated, heat ½ tablespoon of the oil l in a large wok or large skillet over medium-high heat, for 1 minute or until shimmering.
Once the oil has heated, remove the chicken from the marinade, letting the excess marinade drip back into the bowl, and add the chicken to the heated pan. Stir fry the chicken until nearly cooked through and golden, about 2 minutes. Remove the chicken from the pan to a clean plate and wipe out the pan with a paper towel.
Add the remaining ½ tablespoon of oil to the same pan and heat for another minute. Add in sliced mushrooms and stir fry for 1 minute. Add in carrots and snow peas and stir-fry until crisp tender but still bright in color, about 2-3 minutes.
Give the prepared sauce another quick whisk to combine, then add to the skillet, along with the cooked chicken, and bamboo shoot strips. Simmer, stirring constantly, until thickened and glossy. This should only take about 2 minutes.
Serve over rice or cauliflower rice as desired.
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Notes
Storage: Store leftover, cooled stir-fry in an air-tight container for up to 3 days in the refrigerator. To reheat, microwave individual servings or heat in a dry skillet over medium heat until warmed through. Vegetables: Feel free to use any vegetables that have similar cooking times to the mushrooms and carrots, such as peppers, onions, edamame, or green beans.Mirin: The best substitute would be sherry or marsala wine, but if you don't have that on hand, feel free to use rice wine vinegar or rice vinegar. You may also want to add a pinch of sugar to balance out the acidity in the vinegar.Oil: Peanut oil has a high smoking point, so it is perfect for this stir-fry. If you don't have peanut oil, use vegetable oil or canola oil.