Peel, then cut carrot into ¼-inch half-moons. Cut bok choy into 1-inch pieces. Pat chicken dry with paper towels, then cut into 1-inch pieces. Sprinkle half the Moo Shu Spice Blend over chicken, then season with salt and pepper.
Heat a large non-stick pan over medium-high heat. When hot, add peanuts to the dry pan. Toast, stirring often, until golden, 2-3 min. (TIP: Keep your eye on peanuts so they don't burn!) Transfer to a plate.
Add 1 tbsp oil to the same pan, then chicken. (NOTE: Don't overcrowd the pan; cook chicken in 2 batches for 4 ppl, using 1 tbsp oil per batch.) Cook, stirring occasionally, until golden and cooked through, 4-5 min.** Transfer chicken to a plate. Meanwhile, add 10 cups water and 1 tbsp salt to a large pot (use same for 4 ppl). Cover and bring to a boil over high heat.
Reduce heat of the pan to medium, then add carrots. Cook, stirring often, 1-2 min. Add bok choy. Cook, stirring often, until veggies are tender-crisp, 1-2 min. Add chicken, vegetarian oyster sauce, honey-garlic sauce, ¼ tsp (½ tsp) sugar, 2 tbsp (4 tbsp) water and remaining Moo Shu Spice Blend. Cook, stirring often, until sauce thickens, 2-3 min. Remove from heat.
Meanwhile, add noodles to the boiling water. Cook uncovered, until tender, 1-2 min. Drain noodles, then rinse under warm water. Drain well, then return to the pot.
Add half the peanuts and stir-fry mixture to the pot with noodles. Toss to combine. Divide noodles between bowls. Sprinkle remaining peanuts over top.