Roughly chop the onions and the tomatoes.
Heat the olive oil into a pan, add the chopped onions and cook until tender, followed by the tomatoes, garlic, salt, pepper and vegetable stock powder. Cook for 5 minutes then add the basil and some water (up to 1 cup). Cover with a lid and simmer for 10-15 minutes.
Blend then pass the soup through a sieve to achieve a smooth texture and set aside while making the cheesy sauce.
In a small pan combine nutritional yeast, corn flour and coconut oil into a paste. Add the milk a bit at a time whisking the sauce to avoid creating any lumps. Stir in the garlic powder and the lemon juice and heat the sauce on a stove until it thickens.
Serve the soup topped with the cheesy sauce, black pepper and fresh basil leaves.