Mix together peanut butter, soy sauce, black vinegar, sugar, and sesame oil in a small bowl until sauce is well combined. Set aside.

Bring a large pot of water to a boil. Stir in udon noodles and cook for 5 minutes. Add shrimp to the pot of boiling noodles and cook until shrimp are pink and opaque, about 3 minutes. Turn the heat off and leave the pot on the burner. Stir in broccoli; cover and let sit for 2 to 3 minutes.

Drain noodle mixture and transfer to a large serving bowl. Pour sauce on top; stir to coat evenly. Garnish with peanuts to serve.