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, vegetable broth and water. Bring to a boil and allow to cook for about 20 minutes, 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 and enjoy!