Dice the green onions, and set aside all but 1 tablespoon. Slice the mushrooms, and set aside all but 1 tablespoon. Finely chop the 1 tablespoon of green onions and 1 tablespoon of sliced mushrooms, and place in a bowl with the ground pork, 1 tablespoon sesame oil, 1 tablespoon soy sauce, egg, bread crumbs, salt, and pepper. Stir to thoroughly mix the pork filling.
Spoon about 1 tablespoon of the pork filling onto the center of each wonton wrapper. Use your finger or a pastry brush to lightly moisten the edges of the wonton wrappers with water. Fold one corner of the wrapper over the filling onto the opposite corner to form a triangle. Press the edges together to seal. Moisten the two long ends of the triangle, fold them together, and press them firmly to seal.
Bring the chicken broth to a boil in a large saucepan over medium heat. Drop the wontons, one by one, into the broth, and let them cook for 3 to 5 minutes, until they float to the surface. Reduce heat to a simmer, and gently stir in the shrimp, bok choy, and reserved sliced mushrooms. Let the soup simmer 2 more minutes, until the shrimp turn pink, and then drop in the snow pea pods. Garnish with the remaining green onions and a dash of soy sauce and sesame oil, and serve immediately.
