Heat the olive oil in a large stock pot over medium heat.
Add the onion and garlic and cook until fragrant, about 3 minutes.
Add the salt, pepper, smoked paprika, turmeric and dried thyme, stir to combine and cook another 2-3 minutes until onion is translucent but not brown.
Add the cubed potatoes and carrots and stir to coat in oil.
Add the vegetable stock, oat milk and vegan cheese and stir to combine.
Bring soup to a boil, then reduce heat to a rapid simmer and allow to cook for about 15 minutes, until potatoes are cooked through and tender when pierced with a fork.
While the soup simmers, place the frozen broccoli in a colander and run under water until it is defrosted. If broccoli is too large, cut into bite-sized florets.
Carefully add the contents of the stock pot to a blender, secure the lid and blend until creamy (you may need to do this in batches).
Return blended soup to stock pot, set burner to medium heat, add broccoli florets, stir to combine and simmer for another 5 minutes or so, allowing broccoli to cook through.
Taste the soup and add more salt and pepper if needed.
Ladle into bowls and enjoy!
