In a wok or large frying pan, heat the sesame oil over medium heat. Toss in the minced garlic and ginger and saute for 1-2 minutes. If using, crack the eggs into the pan and stir until just cooked.
Pour the brown rice into the pan and stir to combine. Pan fry the rice for about 4 minutes, or until it's heated through, stirring occasionally to keep it from burning. Add in the frozen vegetables and stir to combine. Pour in the rice vinegar and soy sauce and stir the whole thing together. Continue to cook for another 2 minutes to allow all of the flavors to meld together.
Remove from heat, sprinkle in the chives, and serve.