Prepare rice noodles according to package instructions. Rinse under cool water and set aside.
While waiting for the water to boil for the rice noodles, add the sauce ingredients to a small skillet set over medium-low heat. Stir continually until the peanut butter is melted and the sauce is heated through, approximately 3-4 minutes. Remove from heat and set aside.
Add the sesame oil to a large non-stick skillet set over medium heat. Add the shallot, white part of the green onions, carrots, and red pepper. Cook, stirring frequently until the vegetables are crisp, tender, and develop some color, approximately 4-5 minutes.
Push the vegetables to one side of the skillet with a spatula. Add the whisked eggs to the other side. Cook, stirring and chopping frequently with the spatula, until the eggs are cooked through and broken into very small pieces, approximately 4-5 minutes.
Add the prepared rice noodles, one-third cup chopped peanuts, and the warm sauce to the skillet and stir to combine.
Transfer to individual serving dishes and top with the remaining roasted peanuts, green onion tops, and fresh cilantro. Serve immediately with lime wedges on the side.