Peel and halve the cucumber and remove the seeds with a teaspoon. Cut the cucumber halves into slices. Quarter the pepper and cut into short, thin strips. Process the carrot into small sticks or grate. Put the vegetables in a large bowl. Roughly chop the peanuts.
Cook the spaghetti in boiling salted water for 12 minutes until al dente. Drain and add to the bowl with the vegetables. Stir in the dressing and divide the noodles into 2 bowls. Garnish with sesame seeds and chopped peanuts.