Cook the rice noodles according to package directions until they are pliable but still firm. Drain the noodles, rinse with cool water to stop the cooking, and set aside.
In a small bowl, whisk together the soy sauce, fish sauce, lime juice, brown sugar, rice vinegar, and sriracha. Set the sauce aside.
Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Add the sliced chicken and cook, stirring occasionally, until browned and cooked through to an internal temperature of 165°F (74°C). Transfer the chicken to a plate.
Add the remaining 1 tablespoon of oil to the skillet. Add the garlic, red bell pepper, carrot, and the white parts of the green onions. Stir-fry for 2-3 minutes until the vegetables are crisp-tender.
Push the vegetables to one side of the skillet. Pour the beaten eggs onto the empty side and scramble until just set, about 30 seconds. Then, mix the eggs in with the vegetables.
Return the cooked chicken to the skillet. Add the cooked noodles, the sauce, the bean sprouts, and the green parts of the green onions. Toss everything together with tongs for 1-2 minutes, until the sauce coats the noodles and everything is heated through.
Divide the pad thai among serving plates. Top with chopped peanuts and fresh cilantro. Serve immediately with lime wedges on the side.