To make the dressing: Heat the oven to 350°F. Put the sesame seeds on a baking sheet and toast them in the oven until golden brown and fragrant, 15 to 20 minutes. Be careful not to overcook them. Put the toasted seeds in a blender.
In a skillet, heat 1 Tbs. of the peanut oil over medium-low heat. Sauté the shallots and garlic until softened, 3 to 5 minutes. Set aside to cool. Add the shallots, garlic, remaining 6 Tbs. peanut oil, sesame oil, soy sauce, rice vinegar, sugar, and chile paste to the sesame seeds in the blender. Blend on high speed just until a thick, rough paste forms, 2 to 3 minutes. Stop blending when most of the seeds have broken up and been puréed. After the paste forms, it will begin to get oily if you continue to purée it, as the seeds begin to give off their oil (see How to use water to create a creamy sauce). If you have time, refrigerate the purée (for up to a day).
To cook and dress the noodles: Bring a large pot of unsalted water to a rolling boil. Gently fluff the noodles and add them to the water, stirring. Return the water to a boil and cook the noodles for just 10 to 30 seconds. (These tiny fresh noodles don’t need much cooking. If it takes a minute or more for the water to come back to a boil, the noodles will already be done.) Drain the noodles immediately and cool them under cold running water. Drain well. Put the cold noodles in a bowl and toss with the peanut oil.
To assemble: When ready to dress the noodles, drain off any oil that has gathered on the top of the purée. If necessary, whisk about 3/4 cup water into the purée to thin it and to reach a creamy consistency; the sauce will lighten in color and become emulsified; add more water as needed. Add the chopped cilantro to the sauce.
In a large bowl, toss the noodles with about half the dressing. Add the snow peas, red pepper, and daikon, and toss to combine (using your hands is easiest). Add more dressing if you like. Put the noodles in a large serving bowl or on individual plates. Garnish with the cilantro leaves, chopped peanuts, and sliced scallions, or pass little bowls of the garnishes at the table.
Your hands are the best mixing tools. Toss lightly to distribute the sauce, but don't be tempted to cut the noodles. The Chinese believe long noodles mean long life.