In a small bowl, mix together the peanut butter, soy sauce, black vinegar, sugar, and sesame oil. Set aside.
Bring a large pot of water to a boil. Stir in the udon noodles and cook for 5 minutes. Add the frozen shrimp to the pot of boiling noodles and cook for about 3 minutes, until the shrimp are pink and opaque. Turn the stove off, but do not remove pot from the heat. Stir in the broccoli, cover, and let sit for 2-3 minutes.
Drain the noodles, broccoli, and shrimp. In a large serving bowl, toss together the noodles, broccoli, shrimp, and the peanut butter sauce. Garnish with chopped peanuts.