Put the noodles in a bowl; cover with warm water and soak at least 20 minutes. Meanwhile, whisk the peanut butter, soy sauce, ginger, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Add the beef and mix with a spoon to combine.
Heat 1 tablespoon peanut oil in a large skillet over high heat. Add the shallots and cook, stirring, until softened, about 4 minutes. Add the broccoli slaw and cook, stirring, until it starts wilting, about 3 minutes. Transfer the vegetables to a medium bowl. Heat the remaining 1 tablespoon peanut oil in the skillet, then add the beef mixture. Cook, stirring occasionally, until browned, about 7 minutes.
Meanwhile, gently stir the noodles to separate. Reserve 1/2 cup soaking water, then drain the noodles. Return the vegetables to the skillet with the beef and stir to combine. Add the noodles, the reserved soaking water and the Sriracha. Cook, gently tossing, until warmed through, about 4 minutes. Top each serving with the cilantro; serve with lime wedges and more Sriracha.