Heat grill or grill pan over medium-high heat. Cook rice noodles according to package directions; drain and set aside.
In a small bowl, whisk together lime juice, 2 tablespoons olive oil, fish sauce, brown sugar, and sliced chile to make the dressing.
Rub steak with remaining 1 teaspoon olive oil. Grill for 2 to 3 minutes per side for medium-rare, basting with 1 tablespoon of the dressing during the final 2 minutes. Transfer to a cutting board and let rest at least 5 minutes.
Use a julienne peeler to slice carrot, cucumber, and watermelon radish into thin strips.
Divide noodles among 4 bowls. Top with julienned vegetables, sliced steak, and fresh herbs. Drizzle with remaining dressing and garnish with chopped peanuts if desired.