Shave the carrots lengthwise into thin strips using a vegetable peeler, and set aside.
Heat 1 teaspoon oil in a small saucepan over medium heat. Add the ginger and minced garlic; sauté 30 seconds. Add chicken broth and the next 5 ingredients (broth through salt); stir until well-blended. Reduce heat, and simmer 7 minutes, stirring occasionally. Remove from heat, and keep warm.
Heat 2 teaspoons oil in a large nonstick skillet coated with cooking spray over medium-high heat. Add bell peppers and snow peas; sauté 5 minutes or until tender. Remove from heat. Combine carrot, peanut butter mixture, bell pepper mixture, and linguine in a large bowl; toss well. Sprinkle with cilantro. Serve warm or at room temperature.