Bring a medium saucepan filled halfway with water to a boil. Once boiling, add in the carrot noodles and broccoli and cook for 2-3 minutes or until carrot noodles are al dente. Drain into a colander and set aside, dividing the broccoli and carrot noodles.
Place a wok or large skillet over medium heat. Once heated, add in half of the sesame oil. Season the chicken strips with salt and pepper and then add them to the pan. Cook for 5 minutes or until no longer pink inside. Set aside.
Add the remaining sesame oil to the pan and add in the broccoli, garlic and ginger. Toss thoroughly, cooking for 3-5 minutes or until broccoli is fork-tender, tossing frequently. Then, add in the cooked chicken and tamari. Toss to combine and then toss in the carrot noodles and toss again.
Divide into two bowls and garnish with sesame seeds.