In a 5- to 6-quart pan over high heat, bring 2 1/2 to 3 quarts water to a boil. Add noodles, stir to separate, and cook until just tender to bite, 3 to 7 minutes. Drain and rinse well with cold water. If desired, cut noodles into shorter lengths for easier serving. Rinse and dry pan.
In the same pan, over medium heat, stir sesame seeds in oil until golden, 2 to 3 minutes. Remove from heat. Add soy sauce, vinegar, sugar, and cayenne; stir until blended. Add noodles and mix until well coated. Add bell pepper, carrots, and green onions; mix gently. Add salt to taste. Mound in a serving dish.