Bring a large pot of water to a boil and salt it. Put the noodles in a large bowl. When the water boils, add enough of the hot water to the bowl to cover the noodles. Stir and then let the noodles soak until they are soft and pliable. Start checking after 3 minutes. Thicker noodles will take longer.
When the noodles are nearly tender, add the sprouts to soak for a few minutes. Reserve ½ cup of the soaking liquid. Drain the noodles and sprouts in a colander. Run everything under cold water for a minute and then shake off excess water.
Whisk together the peanut butter, sugar, fish sauce, 1 tsp of the chiles, and the lime juice in a small bowl. Add ¼ cup of the reserved soaking liquid and continue to whisk. It should be loose and easily coat the back of a spoon. If it is a little thick, whisk in more hot water 1 tbsp at a time. Taste and adjust seasoning, adding more lime juice, chiles, and salt if you'd like.
Combine the noodles and sprouts with half the dressing in a large bowl, tossing gently with two forks. Peel the eggs and halve lengthwise. Garnish the noodles with the eggs, scallions, and peanuts. Serve at room temperature, passing the lime wedges, remaining dressing and chiles at the table.