In a large pan on medium-high heat, heat 1 tablespoon of vegetable oil. Add chicken and sauté until cooked through and browned. Remove cooked chicken from pan.
Slice chicken into strips and set aside.
In the same pan, heat 1 tablespoon of oil and add mushrooms. When the mushrooms start to soften, add broccoli florets and stir-fry until the broccoli is tender. Remove cooked mushrooms and broccoli from the pan and set aside.
Add 1 tablespoon of oil to the pan and sauté garlic and ginger until fragrant. Add sesame oil, soy sauce, chicken broth, flour and stir until smooth.
Return the chicken and vegetables to the saucy pan, stir until heated through.
Garnish with scallion, then serve immediately with rice or noodles or divide into 4 food storage containers and store in the refrigerator. Can be kept refrigerated for up to 4 days.