In a large pot, heat the olive oil over medium heat. Add the chopped onion, and sauté for about 5 minutes until it becomes translucent.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the diced carrots and celery, cooking for another 5 minutes to soften.
Add the diced potatoes, vegetable broth, thyme, smoked paprika, salt, and pepper. Bring the mixture to a boil.
Reduce the heat and let it simmer for 20-25 minutes, or until the potatoes are tender.
Once cooked, use an immersion blender to puree the soup to your desired consistency, either smooth or slightly chunky.
Stir in the plant-based milk and nutritional yeast to give the soup a creamy texture and nutty flavor. Heat through for an additional 5 minutes, adjusting seasoning as needed.
Serve hot, garnished with freshly chopped parsley.
Notes
Adjust seasoning to taste and use any plant-based milk of your choice.