Add the tomatoes to a 4 qt slow cooker. Use one of the cans to measure your non-dairy milk and add to the slow cooker. Add remaining ingredients and stir to combine.
Set slow cooker on low heat and cook for 4-6 hours.
Once cook time has ended, use an immersion blender to puree the soup, ensuring all chunks of ginger, onion and garlic are processed. Alternatively, you can add the soup in batches to a blender and process until smooth.
Ladle into bowls for serving and top with fresh basil if desired. Great as is or served with a grilled cheese sandwich.