Place sliced chicken and 2 tablespoons cornstarch in a ziploc bag; seal and shake to coat.
Heat 1 tablespoon vegetable oil in a wok or a large 12-inch skillet set over high heat. Add the chicken to the heated oil in one single layer; season with salt and pepper and cook for about 6 to 8 minutes or until cooked and browned on all sides. Cook the chicken in batches if your skillet isn’t big enough.
Remove chicken from the wok/skillet and set aside.
To the same skillet, add remaining oil, broccoli, pepper, and mushrooms; cook for 4 minutes or until veggies are tender. Stir in garlic and cook for 20 seconds. Add the chicken back to the skillet.
In the meantime, in a small bowl, whisk together the chicken broth, soy sauce, oyster sauce, rice vinegar, chili paste, cornstarch, and sugar. Pour the sauce over the chicken and veggies and bring to a simmer.
Continue to cook for a couple minutes, or until sauce is thickened.
Remove from heat. Garnish with green onions and sesame seeds, and serve.
Notes
Vegetable Oil: Don't use olive oil. Choose oils with a high smoke point, like vegetable, peanut, sesame, or canola oil. They can handle the heat and won’t break down.
Sauce: Adjust the consistency of your Hunan sauce as per preference. If it's too thick, a splash of chicken broth or water can help to thin it out; for a thicker sauce, a quick cornstarch slurry does the trick.
Veggie Choices: Feel free to get creative with vegetables. Stick to the classics or toss in your favorites for a personal touch. Just ensure they are cut uniformly for even cooking.
Prep Ahead: Adopt the “mise en place” approach, which translates to "everything in its place." Prepping and measuring all ingredients beforehand ensures a smooth cooking experience, especially for stir-fries.
Hot Pan: A hot pan is essential for that perfect stir-fry. Ensure your wok or pan is heated adequately so that ingredients not only sizzle upon contact but continue to do so as they cook. And don't forget to stir.
To store leftovers, place everything in airtight containers and refrigerate for up to 3 days.