Bring a large pot of water to a boil. Add noodles and cook 2 minutes. Drain noodles in a colander and rinse with cold water until cool; set aside. In a small bowl, stir together contents of 2 ramen seasoning packets, 2 Tbsp. water, soy sauce and brown sugar until combined; set aside. Heat 1 Tbsp. oil in a large nonstick skillet over medium-high heat. Add broccoli, onion and carrot and cook 2 minutes, stirring occasionally. Add remaining 1/4 cup water and continue to cook until water has evaporated, and vegetables are tender-crisp, about 2 minutes longer. Transfer vegetables to a medium bowl. Heat remaining 1 Tbsp. oil in skillet. Add chicken and cook about 4 or 5 minutes until browned and cooked through (165°F internal temp). Add corn and green beans and cook 1 minute. Return broccoli-onion-carrot mixture to skillet. Add noodles and soy sauce mixture and cook 2 to 3 minutes, tossing frequently, until evenly seasoned and warmed through.