Heat a large skillet or wok over medium high heat and add 1 tablespoon of the olive oil. Once the oil is hot, add the chicken. Cook until the chicken is browned on all sides and cooked through, about 5 to 6 minutes. Remove to a large bowl or plate and set aside. Pour out and discard any juices that have collected in the bottom of the skillet.
Reduce the heat to medium. Add 1 tablespoon olive oil, the mushrooms, carrots, and bell peppers. Toss to coat the vegetables in the oil, then cook, stirring occasionally, until the mushrooms are browned and the bell peppers and carrot are crisp-tender, about 8 minutes. Stir in the garlic and ginger and cook just until fragrant, about 30 seconds. Remove the vegetables and any juices that have collected in the skillet to the plate with the chicken.
Add 1/2 tablespoon olive oil to the skillet. Add the beaten eggs and cook, using a spatula to constantly stir and break apart the eggs into small pieces. Remove the cooked eggs to the plate with the chicken and vegetables.
Add the remaining 1 1/2 tablespoons olive oil to the skillet and increase the heat to high. Add in the quinoa and stir to coat it with the oil. Spread it into as flat of a layer as you can. Let it cook undisturbed until it’s toasted and golden on the bottom, about 1 to 2 minutes. With a large spatula, flip it in large sections so that fresh, uncooked portions are touching the bottom of the pan. Repeat cooking and flipping 1 to 2 more times, until it’s nicely toasted throughout.
Stir in the soy sauce, sesame oil, and chili garlic sauce and stir until the quinoa is evenly coated. Add the chicken and vegetables along with any of the vegetable juices and edamame. Stir to combine. Stir in the green onions, then reduce the heat to low. Let cook, stirring occasionally, until warmed through, about 1 to 2 minutes. Taste and adjust seasoning as desired (this will vary based on how salty your soy sauce is and how hot you like your stir fry; I usually dash on a bit more soy sauce and a little extra chili sauce). Enjoy immediately.
Store leftovers in the refrigerator for up to 4 days. Rewarm gently in the microwave and season with a little extra soy sauce as desired.
Freeze leftovers for up to 2 months. Let thaw overnight in the refrigerator.