Bring a large pot of water to a boil. Add noodles and cook until barely tender, about 5 minutes; they should retain a hint of chewiness. Drain, rinse with cold water, drain again and toss with a splash of sesame oil.
In a medium bowl, whisk together the remaining 2 tablespoons sesame oil, the soy sauce, rice vinegar, sesame paste, peanut butter, sugar, ginger, garlic and chili-garlic paste.
Pour the sauce over the noodles and toss. Transfer to a serving bowl, and garnish with vegetables, sesame seeds and peanuts.
Set out a small bowl of water. To assemble the pot stickers, divide the vegetable filling among the wonton wrappers, placing about 1 tablespoon (15 mL) of the filling in the center of each wonton wrapper. Take one filled wonton wrapper and dip your finger in the bowl of water. Moisten two sides of the wrapper, fold all sides together, and pinch along the edge to form a seal. Repeat with the remaining filled wrappers.