In a large pot, heat a splash of water or vegetable broth over medium heat. Add the chopped onion, garlic, carrots, and celery. Sauté for about 5 minutes until softened.

Add the diced potatoes, thyme, salt, and pepper. Stir to combine.

Pour in the vegetable broth and bring to a boil. Reduce heat and simmer for about 20 minutes, or until the potatoes are tender.

Remove the pot from heat. Using an immersion blender, blend the soup until smooth. Alternatively, carefully transfer the soup in batches to a regular blender.

Stir in the coconut milk and nutritional yeast, if using. Adjust seasoning as needed.

Ladle the soup into bowls and enjoy hot, garnished with fresh herbs if desired.