Place cauliflower, carrots, garlic, onion, spices, and stock in a large pot. Cover and bring to a boil, then simmer until veggies are soft, about 15 minutes.
.Add in beans, then use an immersion blender to blend mixture until smooth. You could use a regular blender, but it's so much easier with an immersion blender.
Add broccoli to soup and simmer until soft to your liking, about 5-10 minutes. Turn off heat, then use the blender again. I only blend a bit to keep chunks of broccoli in the soup.
Add in dijon, lemon juice, and cheeses. Mix until cheese is melted. Add more almond milk if the soup is too thick.