Boil a large pot of water and cook the soba noodles according to package directions.
If you have a steamer basket, steam the broccoli over top of the boiling noodles for 3-4 minutes until the broccoli has turned bright green but is still firm.
When the noodles have cooked, drain them and rinse them under cold water to remove any excess starch so the noodles don't clump and stick.
To make the sauce, mix together the peanut butter, tamari, rice vinegar, sesame oil, ginger, garlic and water.
Add the noodles back to the pot with the sauce and spinach. Place on a burner over medium low heat. Toss the noodles to coat with sauce until the spinach has just wilted then add the steamed broccoli.
Serve garnished with chopped cilantro and black sesame seeds.