For the noodles: In a medium saucepan, heat the beef stock with the sugar over low heat, stirring, until the sugar is dissolved. Stir in the vinegar and salt. Remove from heat, pour into a freezer-proof bowl and place in the freezer until well chilled.
While the soup is chilling, make the noodles according to the instructions on the package. Rinse well with cold water and massage to remove excess starch. Drain and set aside.
For the salad: Mix together the pear, cucumber, red onion, rice vinegar, mustard, sugar and salt in a small bowl.
To serve: Divide the noodles between 2 large bowls. Pour the cold broth over the noodles. Top each bowl with a handful of the salad. Divide the roast beef and eggs between the bowls. Grind pepper over each egg and sprinkle with sesame seeds and a bit of seaweed. Serve with the rest of the salad on the side.
Add crushed ice to each bowl of noodles to keep it well chilled.