Steam the broccoli until crisp-tender, about 7 minutes.
Put the steamed broccoli, garlic, non-dairy milk, tamari, all-purpose seasoning, salt, and cayenne pepper in a blender and process on low until smooth, making sure to leave air space at top of blender to allow steam to escape.
If the soup is too thick, add more non-dairy milk, 2 tablespoons at a time, to achieve the desired consistency, pulsing or blending briefly after each addition. Put the soup in to a medium soup pot and cook over medium-low heat, until heated through, stirring often. Season with pepper.
Add more non-dairy milk if soup is too thick. Serve immediately in deep soup bowls with whole-grain crackers or crusty bread on the side.