Cut off the broccoli stalks and set aside for another use (such as in a vegetable stir-fry). Cut the florets into small pieces and steam them until tender-crisp, about 2 to 3 minutes. Refresh florets under cold running water and drain. Set aside.
Cook the udon until tender but still chewy, 8 to 12 minutes. Perform step 3 while the udon is cooking. Drain and rinse under cold water to halt the cooking process. Drain thorougly.
In a blender or food processor, blend the unsalted peanut butter, freshly grated ginger, minced garlic, tamari, brown rice vinegar, maple syrup and cayenne pepper together until smooth, using just enough water to create a medium-thick consistency.
Immediately place the noodles in a bowl or storage container and toss with the peanut sauce. Add the broccoli.