Bring 8 cups water to boil in large saucepan. Add the snow peas and carrots and cook until slightly soft, 30 seconds. Drain well and set aside.
In a separate pot, cook the spaghetti according to package instructions. Drain, rinse with cold water and toss with a 1 tablespoon of the sesame oil.
Combine the remaining 1 tablespoon sesame oil, the peanut butter, soy sauce, rice wine vinegar, brown sugar, chile-garlic paste, ginger, garlic, lime juice and 3 tablespoons hot water in a bowl; stir together until well blended.
Toss the noodles with the sauce. Add the cilantro, peanuts, black sesame seeds and green onions and toss until well mixed. Serve cold or at room temperature.