Make the broth for the soup by combining the chicken - scallions in a large pot. Cover with enough water to cover the chicken. Cover the pot and bring to a boil over high heat. Reduce heat to low and simmer for 1 hour. Remove the chicken and let cool. Strain the broth, discarding the green onion, garlic, black pepper, and ginger. Return soup to the pot and skim the fat.

Meanwhile, make the noodles. Combine the flour - vegetable oil in the bowl of stand mixer. Knead on low for 3 minutes; the dough should be smooth and elastic. Remove dough from the bowl and cover with plastic wrap. Let stand 30 minutes.

Combine half of the sliced zucchini with 2 teaspoon salt in a medium bowl. Let stand 20-30 minutes.

Remove the skin from the chicken and shred. Season with salt and pepper and set aside.

Make the sauce for the soup by combining the soy sauce - ½ teaspoon sesame seeds. Set aside.

Add the sliced potato to the soup. Bring back to a boil over medium-high heat, covering the pot. Reduce heat to low and let simmer for another 20 minutes or until potatoes are done.

Generously dust work surface with flour. Unwrap dough and place on the counter. Using a rolling pin, roll out the dough until paper thin, dusting more flour on the counter and dough when it starts to stick. Fold the dough into thirds, dusting more flour on the dough after each fold. Use a sharp knife and cut ¼ inch wide strips. Unfold the strips and dust flour on the noodles to prevent them from sticking. Set aside.

Return to the salted zucchini. Rinse the zucchini with water and squeeze out any moisture. Heat 1 teaspoon oil in a nonstick pan. Add the zucchini and saute for 1-2 minutes or until cooked. Remove from heat and set aside.

Add the other reserved zucchini to the soup. Bring the soup back to a boil over high heat. Add the noodles and stir to prevent the noodles from sticking to one another. Cook for 1-2 minutes or until done. Remove from heat. Immediately portion the noodles into two bowls with soup, potatoes, and zucchini. Top with the shredded chicken and sauteed zucchini. Garnish with sesame seeds and green onions. Serve with sauce on the side.