In a large pot, warm olive oil over medium heat. Add the onion and cook for about 3 minutes, until translucent. Add the garlic, carrot, and potato, then continue to cook for 2 more minutes.
To the pot, add the oregano and tomato paste then stir to combine. Cook for a few minutes then add the chopped broccoli, and vegetable broth. Bring to a boil and allow to cook for about 15 minutes, just until broccoli and potato are tender. Set aside to cool for a few minutes.
To a high speed blender, add the contents of the pot. If you like a chunkier texture, reserve about 1/2 of the broccoli in the pot. Add the nutritional yeast, lemon juice and non-dairy milk to the blender then blend on high until smooth.
Pour the soup back into the pot and warm over low heat. Cook until heated through. Add salt & pepper to taste. Serve warm with shredded cheese and croutons, and enjoy!
You may need more than 3 cups broth but I recommend starting with that and adding more as needed.