Cook noodles according to package directions; drain.
Heat a medium saucepan over medium heat. Add oil to pan; swirl to coat. Add ginger and garlic; cook 1 minute, stirring constantly. Add stock and soy sauce; bring to a boil. Simmer 10 minutes.
Place carrots, bell pepper, and cucumber in a bowl; toss to combine. Divide noodles evenly among 4 serving bowls; top each serving with one-fourth of vegetable mixture. Pour about 3/4 cup warm stock mixture into each bowl. Sprinkle evenly with herbs and peanuts; drizzle chili oil over top.