Heat the toasted sesame oil in a large skillet or wok over medium-high heat. Add the minced garlic and stir until fragrant, about 30 seconds.
Add the chilled quinoa and frozen mixed vegetables into the skillet. Cook until the vegetables start to soften and the quinoa is well coated with the garlic oil, approximately 2 minutes.
Push the quinoa and vegetable mixture to one side of the skillet. Crack the eggs into the cleared space and scramble them until fully cooked. Then, mix the scrambled eggs into the quinoa and vegetables.
Drizzle the soy sauce over the skillet and sprinkle with ground ginger. Toss everything together and cook for an additional 1 to 2 minutes until the dish is heated through. Taste and adjust the seasonings.