In a large stock pot, heat olive oil. Add onions and leeks. Sweat the onions until soft and translucent but not browned.
Add garlic and continue cooking for 1-2 minutes until garlic becomes fragrant.
Add the dry vermouth to deglaze the pot and boil down the liquid by half.
Add broccoli, potato, and all herbs and spices to pot and stir until herbs and spices become fragrant.
Add stock to the pot and simmer for 40 minutes (more or less) until veggies become very tender.
Remove from heat and stir in vinegar and soy sauce. In a blender, puree the soup in batches. Strain through a sieve for a smoother product. Add the grated cheese and stir in until well blended.