In a bowl, combine sliced chicken with 1 tablespoon soy sauce, 1 tablespoon cornstarch, and a pinch of salt. Mix well and let marinate for at least 15 minutes to enhance flavor.

Warm 1 tablespoon of olive oil in a large skillet over medium-high heat until it begins to shimmer. Carefully add the marinated chicken pieces, spreading them evenly. Cook, stirring occasionally, until the chicken turns a rich golden brown and is fully cooked through, approximately 5 to 7 minutes. Ensure no pink remains.

After removing the chicken from the skillet, set it aside on a plate. Pour the remaining olive oil into the skillet over medium heat. Add the minced garlic and ginger, stirring continuously. Sauté these aromatics until they release their fragrance and turn slightly golden, approximately 30 seconds, ensuring they do not burn.

Place the broccoli florets into the heated skillet, stirring them continuously over medium-high heat for 3-4 minutes. Watch for them to become a vibrant green and achieve a tender-crisp texture. This method helps maintain their natural crunch and ensures they do not become overly soft or lose their appealing color.

In a small bowl, combine the remaining soy sauce, chicken broth, sugar, and cornstarch. Stir the mixture thoroughly until it becomes smooth and free of lumps. This ensures the sauce will have a silky texture and prevents any gritty consistency when added to the stir fry.

Return the chicken to the skillet with the broccoli. Pour the sauce over the top, stirring constantly until it thickens and coats the chicken and broccoli evenly, about 2 minutes.

Pour sesame oil evenly over the stir fry, ensuring it coats all ingredients. Stir thoroughly to integrate the oil, which will impart a nutty aroma. Continue stirring for about 2 minutes over medium heat, allowing the oil to meld with the other flavors, enhancing the dish's aromatic profile.

Sample the stir fry to evaluate the seasoning, adding salt if necessary to enhance the overall taste. Adjust the balance of flavors by incorporating more salt gradually, ensuring the dish achieves a harmonious blend. Check that the seasoning complements the chicken and broccoli without overpowering their natural flavors.

Remove the stir fry from the heat and let it sit undisturbed for one minute. This resting period allows the flavors to integrate fully, ensuring the sauce adheres nicely to the chicken and broccoli, enhancing the overall texture and taste of the dish.

Transfer the chicken and broccoli stir fry to a serving dish while still hot. For an appealing presentation and a delightful contrast in texture, consider garnishing with sesame seeds or thinly sliced green onions. This will enhance the visual appeal and provide a subtle crunch.