In Wok, heat oil over medium-high heat. Add chicken; cook until lightly browned, about 3 min per side.
Meanwhile, reserve 1 tbsp seasoning and set aside. In a bowl, whisk together remaining seasoning, broth, and crushed tomatoes. Add to wok once chicken has browned.
Reduce heat; stir to coat. Cover; simmer, stirring occasionally, until chicken is cooked through, about 5 min.
Meanwhile, using 4-in-1 Mandoline fitted with 6 mm julienne plate, julienne zucchinis into long thin strips to make zoodles (you should have about 6 cups). Place in Multipurpose Steamer; sprinkle with reserved 1 tbsp seasoning. Cover; microwave on high 2 min. Toss (with lid on) and microwave an additional 2 min.
Divide zoodles and chicken on plates, spoon sauce on top and finish with cheese, if desired.