Prepare the vegetables by peeling and cubing the carrots, celery, and potatoes into uniform pieces, finely chop the onion and set aside.

In a large soup pot, heat 2 tablespoons of olive oil over medium heat. Add the chopped onion and a pinch of salt, cooking for about 5 minutes until translucent.

Stir in the diced carrots and sliced celery, cooking for another 5 minutes while stirring occasionally. Add enough vegetable broth to cover the vegetables.

Bring the mixture to a gentle simmer, reduce the heat to low, cover, and let cook for about 20 minutes until the vegetables are tender.

Use an immersion blender to puree the soup to your desired consistency, whether smooth or rustic.

Stir in a splash of coconut milk or heavy cream, season with thyme, rosemary, pepper, and salt, and simmer for an additional 10 minutes.

Ladle the soup into warm bowls, garnishing with chopped parsley before serving.