Mix 1 Tablespoon avocado oil with the tamari, garlic, ginger, salt, and pepper in a large mixing bowl.
Cube the chicken and add it to the bowl, mixing and coating evenly. Set aside.
Meanwhile, bring the water and salt to a boil in a large pot over high heat.
Once boiling, add the soba noodles and cook for about 7 minutes, or until tender. Drain, rinse with cold water, then toss with the toasted sesame oil.
While the noodles cook, thinly slice the cabbage, chop the green onions, and slice the red bell pepper. Measure out the matchstick carrots and sugar snap peas, place all of the vegetables in a bowl, and set aside.
Heat the remaining 1 Tablespoon avocado oil in a skillet over medium-high heat. Add the seasoned chicken and cook for 8-10 minutes, stirring halfway and cooking until the internal temperature reaches 165 degrees F.
While the chicken is cooking, whisk the sauce.
Once the chicken is done, remove it from the pan and add the water and all of the vegetables to that same pan. Quickly stir, then cook until the cabbage has reduced to about half in size and the vegetables are just slightly tender, for about 5-7 minutes.
Pour the sauce over the vegetables, add the noodles and chicken, and gently stir until everything is incorporated. Cook for 2-3 minutes until the sauce thickens and begins to look glossy.
Make the optional drizzle by combining the ingredients and whisking together until smooth.
Divide the Chicken Lo Mein into 6 bowls, drizzle with sauce, add garnishes and enjoy!