In a blender or food processor, blend all pad thai dressing ingredients until smooth and set aside
In a large skillet, warm 2 tablespoons sesame oil over medium heat. Add the sweet potato and carrot and toss until coated. Continue cooking over medium heat for 5 minutes, stirring often.
In a small bowl, whisk the eggs. Using a spoon move the noodles to the side to create a “hole” in the center of the sweet potatoes. Gently pour the whisked eggs into the hole. Allow to set for 30 seconds, then gently stir the egg until cooked through, about one minute. Combine the egg with the noodles, then add the chicken to warm through. Remove from heat and toss liberally with pad thai dressing.
Divide pad thai between plates or bowls and top with cilantro, scallion, and lime wedges. Serve immediately.