Add the chopped onions, chopped garlic, extra virgin olive oil, salt, and dried thyme to a large pot on the stove set to medium heat.
Cook, stirring often, for five minutes or until the onions are softened.
Add the chopped asparagus, turnips, and water to the pot, then bring to a simmer.
Reduce the heat to low-medium, then continue to simmer for 30 minutes or until the vegetables are fork tender.
Add the nutritional yeast to the pot (optional).
Remove some asparagus tips from the pot and reserve them to use as a garnish, if desired.
Let the soup cool off a bit, then transfer it, in batches, to a blender or food processor, and then blend until smooth (or use an immersion blender to blend the soup right in the pot).
Garnish each bowl with a few of the reserved asparagus tips, if desired, and some black pepper, then serve hot.