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Step 1
In a small bowl, stir together the garlic, ginger, soy sauce, vinegar, sesame oil, and honey. Set aside.
Step 2
Trim any excess fat off the chicken then cut into bite-sized pieces. Add chicken to a bowl then drizzle with ¼ cup of the sauce, reserving the remaining sauce for later. Stir the chicken to coat with the sauce then set aside to marinate while you prepare the vegetables.
Step 3
Trim the ends off the carrots then cut into thin strips or “matchsticks." Discard the mushroom stems then thinly slice the mushroom tops. Trim the bottom and the dark green parts from the leeks, slice the remaining portion in half lengthwise, and then into 1/2 inch half-moons. Place in a strainer and then run under cold water to clean away any dirt stuck in the layers. Pat the leeks dry.
Step 4
Heat one tablespoon of oil in a large skillet or sauté pan over medium-high heat. Once hot, brown the chicken on both sides. About 6-8 minutes. Remove cooked chicken to a plate.
Step 5
Wipe out any burn bits on the bottom of the pan then return the pan to the heat and add the remaining tablespoon of oil. Add the carrots and mushrooms. Cook, stirring occasionally, for 4 minutes or until the veggies begin to soften and brown around the edges. If the vegetables are getting too brown, lower the heat to medium.
Step 6
Add the leeks, broccoli, and black pepper. Continue to cook until the leeks are lightly browned and broccoli is bright green, about 4 minutes.
Step 7
Once vegetables are tender, add the chicken back to the pan. Pour in the remaining sauce and stir to combine. Add ¼ cup of the chicken broth or water and simmer for 1 to 2 minutes to thicken the sauce. If your pan is dry or you want more sauce, add the remaining ¼ cup of liquid.
Step 8
Serve the stir fry over rice or quinoa with sesame seeds, sliced scallion, and/or hot sauce, as desired.